Pub Date : 2026-01-12DOI: 10.1016/j.jpaa.2026.108173
Shengding Sun , Aljaž Zalar
The matrix Fejér-Riesz theorem characterizes positive semidefinite matrix polynomials on the real line. In [28] this was extended to the characterization on arbitrary closed semialgebraic sets by using matrix quadratic modules from real algebraic geometry. In the compact case there is a denominator-free characterization, while in the non-compact case denominators are needed except when K is the whole line, an unbounded interval, a union of two unbounded intervals, and according to a conjecture of [28] also when K is a union of an unbounded interval and a point or a union of two unbounded intervals and a point. In this paper, we confirm this conjecture by solving the truncated matrix-valued moment problem on a union of a bounded interval and a point. The presented technique for solving the corresponding moment problem can potentially be used to determine degree bounds in the positivity certificates for matrix polynomials on compact sets K[28, Theorem C].
{"title":"Matrix Fejér-Riesz type theorem for a union of an interval and a point","authors":"Shengding Sun , Aljaž Zalar","doi":"10.1016/j.jpaa.2026.108173","DOIUrl":"10.1016/j.jpaa.2026.108173","url":null,"abstract":"<div><div>The matrix Fejér-Riesz theorem characterizes positive semidefinite matrix polynomials on the real line. In <span><span>[28]</span></span> this was extended to the characterization on arbitrary closed semialgebraic sets <span><math><mi>K</mi><mo>⊆</mo><mi>R</mi></math></span> by using matrix quadratic modules from real algebraic geometry. In the compact case there is a denominator-free characterization, while in the non-compact case denominators are needed except when <em>K</em> is the whole line, an unbounded interval, a union of two unbounded intervals, and according to a conjecture of <span><span>[28]</span></span> also when <em>K</em> is a union of an unbounded interval and a point or a union of two unbounded intervals and a point. In this paper, we confirm this conjecture by solving the truncated matrix-valued moment problem on a union of a bounded interval and a point. The presented technique for solving the corresponding moment problem can potentially be used to determine degree bounds in the positivity certificates for matrix polynomials on compact sets <em>K</em> <span><span>[28, Theorem C]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108173"},"PeriodicalIF":0.8,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981622","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 : 2026-01-08DOI: 10.1016/j.jpaa.2026.108170
J. Reina
This paper establishes a relation between two invariants of 3-dimensional manifolds: the chromatic spherical invariant and the Hennings-Kauffman-Radford invariant HKR. We show that, for a spherical Hopf algebra H, the invariant associated to the pivotal category of finite-dimensional H-modules is equal to the invariant HKR associated to the Drinfeld double of the same Hopf algebra.
{"title":"Chromatic spherical invariant and Hennings invariant of 3-dimensional manifolds","authors":"J. Reina","doi":"10.1016/j.jpaa.2026.108170","DOIUrl":"10.1016/j.jpaa.2026.108170","url":null,"abstract":"<div><div>This paper establishes a relation between two invariants of 3-dimensional manifolds: the chromatic spherical invariant <span><math><mi>K</mi></math></span> and the Hennings-Kauffman-Radford invariant HKR. We show that, for a spherical Hopf algebra <em>H</em>, the invariant <span><math><mi>K</mi></math></span> associated to the pivotal category of finite-dimensional <em>H</em>-modules is equal to the invariant HKR associated to the Drinfeld double <span><math><mi>D</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> of the same Hopf algebra.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108170"},"PeriodicalIF":0.8,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145950134","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 : 2026-01-01DOI: 10.1016/j.jpaa.2025.108153
Hans Franzen , Gianni Petrella , Rachel Webb
We give an effective characterization of the walls in the variation of geometric invariant theory problem associated to a quiver and a dimension vector.
本文给出了一个几何不变理论问题中与一个颤振和一个维向量相关的壁面变化的有效表征。
{"title":"Finding the walls for quiver moduli","authors":"Hans Franzen , Gianni Petrella , Rachel Webb","doi":"10.1016/j.jpaa.2025.108153","DOIUrl":"10.1016/j.jpaa.2025.108153","url":null,"abstract":"<div><div>We give an effective characterization of the walls in the variation of geometric invariant theory problem associated to a quiver and a dimension vector.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108153"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885249","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 : 2026-01-01DOI: 10.1016/j.jpaa.2025.108168
Ahmed Laghribi, Trisha Maiti
Let F be a field of characteristic 2. The m-Pfister number of a quadratic form is the least number of forms similar to m-fold Pfister forms needed to express φ up to Witt equivalence. Our aim in this note is to discuss the case by giving an inductive formula that explicitly bounds the 3-Pfister number of any form in .
{"title":"On the 3-Pfister number in characteristic 2","authors":"Ahmed Laghribi, Trisha Maiti","doi":"10.1016/j.jpaa.2025.108168","DOIUrl":"10.1016/j.jpaa.2025.108168","url":null,"abstract":"<div><div>Let <em>F</em> be a field of characteristic 2. The <em>m</em>-Pfister number of a quadratic form <span><math><mi>φ</mi><mo>∈</mo><msubsup><mrow><mi>I</mi></mrow><mrow><mi>q</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>(</mo><mi>F</mi><mo>)</mo></math></span> is the least number of forms similar to <em>m</em>-fold Pfister forms needed to express <em>φ</em> up to Witt equivalence. Our aim in this note is to discuss the case <span><math><mi>m</mi><mo>=</mo><mn>3</mn></math></span> by giving an inductive formula that explicitly bounds the 3-Pfister number of any form in <span><math><msubsup><mrow><mi>I</mi></mrow><mrow><mi>q</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mi>F</mi></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108168"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926215","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 : 2026-01-01DOI: 10.1016/j.jpaa.2025.108167
Shahriyar Roshan Zamir
Over an algebraically closed field, the double point interpolation problem asks for the vector space dimension of the projective hypersurfaces of degree d singular at a given set of points. After being open for 90 years, a series of papers by J. Alexander and A. Hirschowitz in 1992–1995 settled this question in what is referred to as the Alexander-Hirschowitz theorem. In this paper we primarily use commutative algebra to lay the groundwork necessary to prove analogous statements in the weighted projective space, a natural generalization of the projective space. We prove the Hilbert function of general simple points in any n-dimensional weighted projective space exhibits the expected behavior. We also introduce an inductive procedure for weighted projective space, similar to that originally due to A. Terracini from 1915, to demonstrate an example of a weighted projective plane where the analogue of the Alexander-Hirschowitz theorem holds without exceptions and prove our example is the only such plane. Furthermore, Terracini's lemma regarding secant varieties is adapted to give an interpolation bound for an infinite family of weighted projective planes.
{"title":"Interpolation in weighted projective spaces","authors":"Shahriyar Roshan Zamir","doi":"10.1016/j.jpaa.2025.108167","DOIUrl":"10.1016/j.jpaa.2025.108167","url":null,"abstract":"<div><div>Over an algebraically closed field, the <em>double point interpolation</em> problem asks for the vector space dimension of the projective hypersurfaces of degree <em>d</em> singular at a given set of points. After being open for 90 years, a series of papers by J. Alexander and A. Hirschowitz in 1992–1995 settled this question in what is referred to as the Alexander-Hirschowitz theorem. In this paper we primarily use commutative algebra to lay the groundwork necessary to prove analogous statements in the <em>weighted projective space</em>, a natural generalization of the projective space. We prove the Hilbert function of general simple points in any <em>n</em>-dimensional weighted projective space exhibits the expected behavior. We also introduce an inductive procedure for weighted projective space, similar to that originally due to A. Terracini from 1915, to demonstrate an example of a weighted projective plane where the analogue of the Alexander-Hirschowitz theorem holds without exceptions and prove our example is the only such plane. Furthermore, Terracini's lemma regarding secant varieties is adapted to give an interpolation bound for an infinite family of weighted projective planes.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108167"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926216","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 : 2026-01-01DOI: 10.1016/j.jpaa.2025.108145
Shamik Das, Somnath Jha
We consider certain families of integers n determined by some congruence condition, such that the global root number of the elliptic curve is 1 for every n, however a given n may or may not be a sum of two rational cubes. We give explicit criteria in terms of the 2-parts and 3-parts of the ideal class groups of certain cubic number fields to determine whether such an n is a cube sum. In particular, we study integers n divisible by 3 such that the global root number of is 1. For example, for a prime , we show that for 3ℓ to be a sum of two rational cubes, it is necessary that the ideal class group of contains as a subgroup. Moreover, for a positive proportion of primes , 3ℓ can not be a sum of two rational cubes. A key ingredient in the proof is to explore the relation between the 2-Selmer group and the 3-isogeny Selmer group of with the ideal class groups of appropriate cubic number fields.
{"title":"On certain root number 1 cases of the cube sum problem","authors":"Shamik Das, Somnath Jha","doi":"10.1016/j.jpaa.2025.108145","DOIUrl":"10.1016/j.jpaa.2025.108145","url":null,"abstract":"<div><div>We consider certain families of integers <em>n</em> determined by some congruence condition, such that the global root number of the elliptic curve <span><math><msub><mrow><mi>E</mi></mrow><mrow><mo>−</mo><mn>432</mn><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub><mo>:</mo><msup><mrow><mi>Y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow><mi>X</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>−</mo><mn>432</mn><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> is 1 for every <em>n</em>, however a given <em>n</em> may or may not be a sum of two rational cubes. We give explicit criteria in terms of the 2-parts and 3-parts of the ideal class groups of certain cubic number fields to determine whether such an <em>n</em> is a cube sum. In particular, we study integers <em>n</em> divisible by 3 such that the global root number of <span><math><msub><mrow><mi>E</mi></mrow><mrow><mo>−</mo><mn>432</mn><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math></span> is 1. For example, for a prime <span><math><mi>ℓ</mi><mo>≡</mo><mn>7</mn><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>9</mn><mo>)</mo></math></span>, we show that for 3<em>ℓ</em> to be a sum of two rational cubes, it is necessary that the ideal class group of <span><math><mi>Q</mi><mo>(</mo><mroot><mrow><mn>12</mn><mi>ℓ</mi></mrow><mrow><mn>3</mn></mrow></mroot><mo>)</mo></math></span> contains <span><math><mfrac><mrow><mi>Z</mi></mrow><mrow><mn>6</mn><mi>Z</mi></mrow></mfrac><mo>⊕</mo><mfrac><mrow><mi>Z</mi></mrow><mrow><mn>3</mn><mi>Z</mi></mrow></mfrac></math></span> as a subgroup. Moreover, for a positive proportion of primes <span><math><mi>ℓ</mi><mo>≡</mo><mn>7</mn><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>9</mn><mo>)</mo></math></span>, 3<em>ℓ</em> can not be a sum of two rational cubes. A key ingredient in the proof is to explore the relation between the 2-Selmer group and the 3-isogeny Selmer group of <span><math><msub><mrow><mi>E</mi></mrow><mrow><mo>−</mo><mn>432</mn><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math></span> with the ideal class groups of appropriate cubic number fields.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108145"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885247","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 : 2026-01-01DOI: 10.1016/j.jpaa.2025.108166
Nikita A. Karpenko
Given a reductive algebraic group G, we introduce a notion of consistent projective G-homogeneous variety X. For instance, the variety of Borel subgroups in G is consistent; if G is of inner type, all projective G-homogeneous varieties are consistent.
Our main result describes the summands in the complete motivic decomposition of X. It extends an earlier result of the author providing the same for G of inner type.
{"title":"Consistent varieties and their complete motivic decompositions","authors":"Nikita A. Karpenko","doi":"10.1016/j.jpaa.2025.108166","DOIUrl":"10.1016/j.jpaa.2025.108166","url":null,"abstract":"<div><div>Given a reductive algebraic group <em>G</em>, we introduce a notion of <em>consistent</em> projective <em>G</em>-homogeneous variety <em>X</em>. For instance, the variety of Borel subgroups in <em>G</em> is consistent; if <em>G</em> is of inner type, all projective <em>G</em>-homogeneous varieties are consistent.</div><div>Our main result describes the summands in the complete motivic decomposition of <em>X</em>. It extends an earlier result of the author providing the same for <em>G</em> of inner type.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108166"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885248","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 : 2025-12-15DOI: 10.1016/j.jpaa.2025.108165
Clémence Chanavat, Amar Hadzihasanovic
We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict ω- categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the expected properties: they include all degenerate cells, are closed under 2-out-of-3, and satisfy an appropriate version of the “division lemma”, which ensures that enwrapping a diagram with equivalences at all sides is an invertible operation up to higher equivalence. On the way to this result, we develop methods, such as an algebraic calculus of natural equivalences, for handling the weak units and unitors which set this framework apart from strict ω- categories.
{"title":"Equivalences in diagrammatic sets","authors":"Clémence Chanavat, Amar Hadzihasanovic","doi":"10.1016/j.jpaa.2025.108165","DOIUrl":"10.1016/j.jpaa.2025.108165","url":null,"abstract":"<div><div>We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict <em>ω</em>-<!--> <!-->categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the expected properties: they include all degenerate cells, are closed under 2-out-of-3, and satisfy an appropriate version of the “division lemma”, which ensures that enwrapping a diagram with equivalences at all sides is an invertible operation up to higher equivalence. On the way to this result, we develop methods, such as an algebraic calculus of natural equivalences, for handling the weak units and unitors which set this framework apart from strict <em>ω</em>-<!--> <!-->categories.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108165"},"PeriodicalIF":0.8,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841223","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 : 2025-12-08DOI: 10.1016/j.jpaa.2025.108148
Marian Aprodu , Andrea Bruno , Edoardo Sernesi
The present paper is a natural continuation of the previous work [2] where we studied the second syzygy scheme of canonical curves. We find sufficient conditions ensuring that the second syzygy scheme of a genus–g curve of degree at least coincides with the curve. If the property is satisfied, the equality is ensured by a more general fact emphasized in [2]. If fails, then the analysis uses the known case of canonical curves.
{"title":"The second syzygy schemes of curves of large degree","authors":"Marian Aprodu , Andrea Bruno , Edoardo Sernesi","doi":"10.1016/j.jpaa.2025.108148","DOIUrl":"10.1016/j.jpaa.2025.108148","url":null,"abstract":"<div><div>The present paper is a natural continuation of the previous work <span><span>[2]</span></span> where we studied the second syzygy scheme of canonical curves. We find sufficient conditions ensuring that the second syzygy scheme of a genus–<em>g</em> curve of degree at least <span><math><mn>2</mn><mi>g</mi><mo>+</mo><mn>2</mn></math></span> coincides with the curve. If the property <span><math><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> is satisfied, the equality is ensured by a more general fact emphasized in <span><span>[2]</span></span>. If <span><math><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> fails, then the analysis uses the known case of canonical curves.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108148"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705835","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 : 2025-12-08DOI: 10.1016/j.jpaa.2025.108157
Jiayi Chen , Bangming Deng , Shiquan Ruan
This paper deals with the triangle singularity defined by the equation for a weight triple , as well as the category of coherent sheaves over the weighted projective line defined by f. We calculate Hall polynomials associated with extension bundles, line bundles and torsion sheaves over . By using derived equivalence, this provides a unified conceptual method for calculating Hall polynomials for representations of tame quivers obtained by Szántó and Szöllősi (2024) [35].
{"title":"Hall polynomials for weighted projective lines","authors":"Jiayi Chen , Bangming Deng , Shiquan Ruan","doi":"10.1016/j.jpaa.2025.108157","DOIUrl":"10.1016/j.jpaa.2025.108157","url":null,"abstract":"<div><div>This paper deals with the triangle singularity defined by the equation <span><math><mi>f</mi><mo>=</mo><msubsup><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>X</mi></mrow><mrow><mn>3</mn></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></msubsup></math></span> for a weight triple <span><math><mo>(</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></math></span>, as well as the category of coherent sheaves over the weighted projective line <span><math><mi>X</mi></math></span> defined by <em>f</em>. We calculate Hall polynomials associated with extension bundles, line bundles and torsion sheaves over <span><math><mi>X</mi></math></span>. By using derived equivalence, this provides a unified conceptual method for calculating Hall polynomials for representations of tame quivers obtained by Szántó and Szöllősi (2024) <span><span>[35]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108157"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145739259","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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