Pub Date : 2025-11-01Epub Date: 2025-10-21DOI: 10.1016/j.jpaa.2025.108113
Ritesh Kumar Pandey, Sachin S. Sharma
In this paper, we extend the notion of Weyl modules for twisted toroidal Lie algebra . We prove that the level one global Weyl modules of are isomorphic to the tensor product of the level one representation of twisted affine Lie algebras and certain lattice vertex algebras. As a byproduct, we calculate the graded character of the level one local Weyl modules of .
{"title":"Weyl modules for twisted toroidal Lie algebras","authors":"Ritesh Kumar Pandey, Sachin S. Sharma","doi":"10.1016/j.jpaa.2025.108113","DOIUrl":"10.1016/j.jpaa.2025.108113","url":null,"abstract":"<div><div>In this paper, we extend the notion of Weyl modules for twisted toroidal Lie algebra <span><math><mi>T</mi><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>. We prove that the level one global Weyl modules of <span><math><mi>T</mi><mo>(</mo><mi>μ</mi><mo>)</mo></math></span> are isomorphic to the tensor product of the level one representation of twisted affine Lie algebras and certain lattice vertex algebras. As a byproduct, we calculate the graded character of the level one local Weyl modules of <span><math><mi>T</mi><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108113"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-10-01DOI: 10.1016/j.jpaa.2025.108102
Kiryong Chung , Jaehyun Kim , Jeong-Seop Kim
Let X be a Fano threefold of index one and degree 22 with . Such a threefold X can be realized as the zero locus of a regular section s of over the Grassmannian , where and is the universal subbundle. When the section s is given by the net of the -invariant skew-symmetric forms, we call it the Mukai-Umemura (MU) variety. In this paper, we prove that the Hilbert scheme of rational quartic curves in the MU-variety is smooth, and we compute its Poincaré polynomial by applying Białynicki-Birula's theorem.
{"title":"Rational quartic curves in the Mukai-Umemura variety","authors":"Kiryong Chung , Jaehyun Kim , Jeong-Seop Kim","doi":"10.1016/j.jpaa.2025.108102","DOIUrl":"10.1016/j.jpaa.2025.108102","url":null,"abstract":"<div><div>Let <em>X</em> be a Fano threefold of index one and degree 22 with <span><math><mrow><mi>Pic</mi></mrow><mo>(</mo><mi>X</mi><mo>)</mo><mo>≅</mo><mi>Z</mi></math></span>. Such a threefold <em>X</em> can be realized as the zero locus of a regular section <strong>s</strong> of <span><math><msup><mrow><mo>(</mo><msup><mrow><mo>⋀</mo></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>U</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>)</mo></mrow><mrow><mo>⊕</mo><mn>3</mn></mrow></msup></math></span> over the Grassmannian <span><math><mrow><mi>Gr</mi></mrow><mo>(</mo><mn>3</mn><mo>,</mo><mi>V</mi><mo>)</mo></math></span>, where <span><math><mi>dim</mi><mo></mo><mi>V</mi><mo>=</mo><mn>7</mn></math></span> and <span><math><mi>U</mi></math></span> is the universal subbundle. When the section <strong>s</strong> is given by the net of the <span><math><msub><mrow><mi>SL</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-invariant skew-symmetric forms, we call it the Mukai-Umemura (MU) variety. In this paper, we prove that the Hilbert scheme of rational quartic curves in the MU-variety is smooth, and we compute its Poincaré polynomial by applying Białynicki-Birula's theorem.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108102"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-09-08DOI: 10.1016/j.jpaa.2025.108084
Himanshu Rewri, Surjeet Kour
In this paper, we study the isotropy group of Lotka-Volterra derivations of , i.e., a derivation d of the form . If or , we show that the isotropy group of d is finite. However, for , it is observed that the isotropy group of d need not be finite. Indeed, for , we identify an infinite collection of automorphisms in the isotropy group of d. Moreover, for , we show that the isotropy group of d is isomorphic to the dihedral group of order 2n.
{"title":"Isotropy group of Lotka-Volterra derivations","authors":"Himanshu Rewri, Surjeet Kour","doi":"10.1016/j.jpaa.2025.108084","DOIUrl":"10.1016/j.jpaa.2025.108084","url":null,"abstract":"<div><div>In this paper, we study the isotropy group of Lotka-Volterra derivations of <span><math><mi>K</mi><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></math></span>, i.e., a derivation <em>d</em> of the form <span><math><mi>d</mi><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo><mo>=</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>−</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>)</mo></math></span>. If <span><math><mi>n</mi><mo>=</mo><mn>3</mn></math></span> or <span><math><mi>n</mi><mo>≥</mo><mn>5</mn></math></span>, we show that the isotropy group of <em>d</em> is finite. However, for <span><math><mi>n</mi><mo>=</mo><mn>4</mn></math></span>, it is observed that the isotropy group of <em>d</em> need not be finite. Indeed, for <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mo>−</mo><mn>1</mn></math></span>, we identify an infinite collection of automorphisms in the isotropy group of <em>d</em>. Moreover, for <span><math><mi>n</mi><mo>≥</mo><mn>3</mn><mo>,</mo><mspace></mspace><mspace></mspace><mtext>and</mtext><mspace></mspace><mspace></mspace><msub><mrow><mi>C</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mn>1</mn></math></span>, we show that the isotropy group of <em>d</em> is isomorphic to the dihedral group of order 2<em>n</em>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108084"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145107308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-10-20DOI: 10.1016/j.jpaa.2025.108115
Teena Gerhardt , Maximilien Péroux , W. Hermann B. Soré
We establish comparison maps between the classical algebraic K-theory of algebras over a field and its analogue , an algebraic K-theory for coalgebras over a field. The comparison maps are compatible with the Hattori–Stallings (co)traces. We identify conditions on the algebras or coalgebras under which the comparison maps are equivalences. Notably, the algebraic K-theory of the power series ring is equivalent to the -theory of the divided power coalgebra. We also establish comparison maps between the G-theory of finite dimensional representations of an algebra and its analogue for coalgebras. In particular, we show that the Swan theory of a group is equivalent to the -theory of the representative functions coalgebra, reframing the classical character of a group as a trace in coHochschild homology.
{"title":"Coalgebraic K-theory","authors":"Teena Gerhardt , Maximilien Péroux , W. Hermann B. Soré","doi":"10.1016/j.jpaa.2025.108115","DOIUrl":"10.1016/j.jpaa.2025.108115","url":null,"abstract":"<div><div>We establish comparison maps between the classical algebraic <em>K</em>-theory of algebras over a field and its analogue <span><math><msup><mrow><mi>K</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span>, an algebraic <em>K</em>-theory for coalgebras over a field. The comparison maps are compatible with the Hattori–Stallings (co)traces. We identify conditions on the algebras or coalgebras under which the comparison maps are equivalences. Notably, the algebraic <em>K</em>-theory of the power series ring is equivalent to the <span><math><msup><mrow><mi>K</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span>-theory of the divided power coalgebra. We also establish comparison maps between the <em>G</em>-theory of finite dimensional representations of an algebra and its analogue <span><math><msup><mrow><mi>G</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span> for coalgebras. In particular, we show that the Swan theory of a group is equivalent to the <span><math><msup><mrow><mi>G</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span>-theory of the representative functions coalgebra, reframing the classical character of a group as a trace in coHochschild homology.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108115"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-10-01DOI: 10.1016/j.jpaa.2025.108104
Justin Fong , Mitsuhiro Miyazaki
The F-pure threshold is the characteristic p counter part of the log canonical threshold in characteristic zero. It is a numerical invariant associated to the singularities of a variety, hence computing its value is important. We give a closed formula for the F-pure threshold of the irrelevant maximal ideal of Schubert cycles, which are the homogeneous coordinate rings of Schubert subvarieties of a Grassmannian. The main point of the computation is to give an explicit formula for the a-invariant of a Schubert cycle. The derivation of both formulas is made possible through the combinatorics of the underlying poset of these rings.
f -纯阈值是特征0中对数正则阈值的特征p计数器部分。它是一个与各种奇点有关的数值不变量，因此计算它的值是很重要的。我们给出了无关极大理想Schubert环的f -纯阈值的一个封闭公式，Schubert环是一类Grassmannian的Schubert子变量的齐次坐标环。计算的重点是给出舒伯特循环的a不变量的显式公式。这两个公式的推导是通过对这些环的基本偏序集的组合而实现的。
{"title":"The F-pure threshold of a Schubert cycle","authors":"Justin Fong , Mitsuhiro Miyazaki","doi":"10.1016/j.jpaa.2025.108104","DOIUrl":"10.1016/j.jpaa.2025.108104","url":null,"abstract":"<div><div>The <em>F</em>-pure threshold is the characteristic <em>p</em> counter part of the log canonical threshold in characteristic zero. It is a numerical invariant associated to the singularities of a variety, hence computing its value is important. We give a closed formula for the <em>F</em>-pure threshold of the irrelevant maximal ideal of Schubert cycles, which are the homogeneous coordinate rings of Schubert subvarieties of a Grassmannian. The main point of the computation is to give an explicit formula for the <em>a</em>-invariant of a Schubert cycle. The derivation of both formulas is made possible through the combinatorics of the underlying poset of these rings.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108104"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-09-10DOI: 10.1016/j.jpaa.2025.108087
Li Guo , Yunnan Li , Yunhe Sheng , Rong Tang
The celebrated Milnor-Moore theorem and the more general Cartier-Kostant-Milnor-Moore theorem establish close interconnections among a connected and a pointed cocommutative Hopf algebra, its Lie algebra of primitive elements, and its group of group-like elements. Crossed homomorphisms for Lie algebras, groups and Hopf algebras have been studied extensively, first from a cohomological perspective and then more broadly, with an important case given by difference operators. In this paper, we show that the relationship among the different algebraic structures captured in the Milnor-Moore theorem can be strengthened to include crossed homomorphisms and difference operators, and we also give a graph characterization of Hopf algebra crossed homomorphisms which is compatible with that of the corresponding Lie algebras via the Milnor-Moore theorem. Finally we obtain a Cartier-Kostant-Milnor-Moore type structure theorem for pointed cocommutative difference Hopf algebras. Examples and classifications of difference operators are provided for several Hopf algebras.
{"title":"Crossed homomorphisms and Cartier-Kostant-Milnor-Moore theorem for difference Hopf algebras","authors":"Li Guo , Yunnan Li , Yunhe Sheng , Rong Tang","doi":"10.1016/j.jpaa.2025.108087","DOIUrl":"10.1016/j.jpaa.2025.108087","url":null,"abstract":"<div><div>The celebrated Milnor-Moore theorem and the more general Cartier-Kostant-Milnor-Moore theorem establish close interconnections among a connected and a pointed cocommutative Hopf algebra, its Lie algebra of primitive elements, and its group of group-like elements. Crossed homomorphisms for Lie algebras, groups and Hopf algebras have been studied extensively, first from a cohomological perspective and then more broadly, with an important case given by difference operators. In this paper, we show that the relationship among the different algebraic structures captured in the Milnor-Moore theorem can be strengthened to include crossed homomorphisms and difference operators, and we also give a graph characterization of Hopf algebra crossed homomorphisms which is compatible with that of the corresponding Lie algebras via the Milnor-Moore theorem. Finally we obtain a Cartier-Kostant-Milnor-Moore type structure theorem for pointed cocommutative difference Hopf algebras. Examples and classifications of difference operators are provided for several Hopf algebras.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108087"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-10-01DOI: 10.1016/j.jpaa.2025.108101
Elad Paran , Thieu N. Vo
We study Noether's normalization lemma for finitely generated algebras over a division algebra. In its classical form, the lemma states that if I is a proper ideal of the ring of polynomials over a field F, then the quotient ring is a finite extension of a polynomial ring over F. We prove that the lemma holds when is the ring of polynomials in n central variables over a division algebra D. We provide examples demonstrating that Noether's normalization may fail for the skew polynomial ring with respect to commuting automorphisms of D. We give a sufficient condition for under which the normalization lemma holds for such ring. In the case where is a field, this sufficient condition is proved to be necessary.
{"title":"Noether's normalization in skew polynomial rings","authors":"Elad Paran , Thieu N. Vo","doi":"10.1016/j.jpaa.2025.108101","DOIUrl":"10.1016/j.jpaa.2025.108101","url":null,"abstract":"<div><div>We study Noether's normalization lemma for finitely generated algebras over a division algebra. In its classical form, the lemma states that if <em>I</em> is a proper ideal of the ring <span><math><mi>R</mi><mo>=</mo><mi>F</mi><mo>[</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></math></span> of polynomials over a field <em>F</em>, then the quotient ring <span><math><mi>R</mi><mo>/</mo><mi>I</mi></math></span> is a finite extension of a polynomial ring over <em>F</em>. We prove that the lemma holds when <span><math><mi>R</mi><mo>=</mo><mi>D</mi><mo>[</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></math></span> is the ring of polynomials in <em>n</em> central variables over a division algebra <em>D</em>. We provide examples demonstrating that Noether's normalization may fail for the skew polynomial ring <span><math><mi>D</mi><mo>[</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>;</mo><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></math></span> with respect to commuting automorphisms <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> of <em>D</em>. We give a sufficient condition for <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> under which the normalization lemma holds for such ring. In the case where <span><math><mi>D</mi><mo>=</mo><mi>F</mi></math></span> is a field, this sufficient condition is proved to be necessary.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108101"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-09-11DOI: 10.1016/j.jpaa.2025.108089
Thomas Michael Keller , Gavin Pettigrew , Saskia Solotko , Lixin Zheng
For a finite group G, the vertices of the prime graph are the primes that divide , and two vertices p and q are adjacent if and only if there is an element of order pq in G. Prime graphs of solvable groups as well as groups whose noncyclic composition factors have order divisible by exactly three distinct primes have been classified in graph-theoretic terms. In this paper, we begin to develop a general theory on the existence of edges in the prime graph of an arbitrary T-solvable group, that is, a group whose composition factors are cyclic or isomorphic to a fixed nonabelian simple group T. We then apply these results to classify the prime graphs of T-solvable groups for, in a suitable sense, most T such that has exactly four prime divisors. We find that these groups almost always have a 3-colorable prime graph complement containing few possible triangles.
{"title":"Classifying prime graphs of finite groups – a methodical approach","authors":"Thomas Michael Keller , Gavin Pettigrew , Saskia Solotko , Lixin Zheng","doi":"10.1016/j.jpaa.2025.108089","DOIUrl":"10.1016/j.jpaa.2025.108089","url":null,"abstract":"<div><div>For a finite group <em>G</em>, the vertices of the prime graph <span><math><mi>Γ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> are the primes that divide <span><math><mo>|</mo><mi>G</mi><mo>|</mo></math></span>, and two vertices <em>p</em> and <em>q</em> are adjacent if and only if there is an element of order <em>pq</em> in <em>G</em>. Prime graphs of solvable groups as well as groups whose noncyclic composition factors have order divisible by exactly three distinct primes have been classified in graph-theoretic terms. In this paper, we begin to develop a general theory on the existence of edges in the prime graph of an arbitrary <em>T</em>-solvable group, that is, a group whose composition factors are cyclic or isomorphic to a fixed nonabelian simple group <em>T</em>. We then apply these results to classify the prime graphs of <em>T</em>-solvable groups for, in a suitable sense, most <em>T</em> such that <span><math><mo>|</mo><mi>T</mi><mo>|</mo></math></span> has exactly four prime divisors. We find that these groups almost always have a 3-colorable prime graph complement containing few possible triangles.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108089"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145107305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-10-01DOI: 10.1016/j.jpaa.2025.108103
Natsume Kitagawa
Corti defined the notion of standard models of del Pezzo fibrations, and studied their existence over with a fixed generic fibre in [6]. In this paper, we prove the existence of standard models of del Pezzo fibrations of degree 4 in characteristic >2. To show this, we use the notion of Kollár stability, which was introduced in [12] and [1].
{"title":"On the standard models of del Pezzo fibrations of degree four","authors":"Natsume Kitagawa","doi":"10.1016/j.jpaa.2025.108103","DOIUrl":"10.1016/j.jpaa.2025.108103","url":null,"abstract":"<div><div>Corti defined the notion of standard models of del Pezzo fibrations, and studied their existence over <span><math><mi>C</mi></math></span> with a fixed generic fibre in <span><span>[6]</span></span>. In this paper, we prove the existence of standard models of del Pezzo fibrations of degree 4 in characteristic >2. To show this, we use the notion of Kollár stability, which was introduced in <span><span>[12]</span></span> and <span><span>[1]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108103"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145333342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-10-22DOI: 10.1016/j.jpaa.2025.108117
J. Miguel Calderón
In this article, we describe the lattice of ideals of some Green biset functors. We consider Green biset functors which satisfy that each evaluation is a finite-dimensional split semisimple commutative algebra and use the idempotents in these evaluations to characterize any ideal of these Green biset functors. For this we will give the definition of MC-group, this definition generalizes that of a B-group, given for the Burnside functor.
Given a Green biset functor A, with the above hypotheses, the set of all MC-groups of A has a structure of a poset and we prove that there exists an isomorphism of lattices between the set of ideals of A and the set of upward closed subsets of the MC-groups of A.
{"title":"Ideals of some Green biset functors","authors":"J. Miguel Calderón","doi":"10.1016/j.jpaa.2025.108117","DOIUrl":"10.1016/j.jpaa.2025.108117","url":null,"abstract":"<div><div>In this article, we describe the lattice of ideals of some Green biset functors. We consider Green biset functors which satisfy that each evaluation is a finite-dimensional split semisimple commutative algebra and use the idempotents in these evaluations to characterize any ideal of these Green biset functors. For this we will give the definition of <em>MC</em>-group, this definition generalizes that of a <em>B</em>-group, given for the Burnside functor.</div><div>Given a Green biset functor <em>A</em>, with the above hypotheses, the set of all <em>MC</em>-groups of <em>A</em> has a structure of a poset and we prove that there exists an isomorphism of lattices between the set of ideals of <em>A</em> and the set of upward closed subsets of the <em>MC</em>-groups of <em>A</em>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108117"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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