Pub Date : 2026-02-10DOI: 10.1016/j.aim.2026.110830
Quan Situ
The hybrid quantum group was firstly introduced by Gaitsgory, whose category can be viewed as a quantum analogue of BGG category . We give a coherent model for its principal block at roots of unity, using the non-commutative Springer resolution defined by Bezrukavnikov–Mirković. In particular, the principal block is derived equivalent to the affine Hecke category. As an application, we endow the principal block with a canonical grading, and show that the graded multiplicity of simple module in Verma module is given by the generic Kazhdan–Lusztig polynomial.
{"title":"Category O for hybrid quantum groups and non-commutative Springer resolutions","authors":"Quan Situ","doi":"10.1016/j.aim.2026.110830","DOIUrl":"10.1016/j.aim.2026.110830","url":null,"abstract":"<div><div>The hybrid quantum group was firstly introduced by Gaitsgory, whose category <span><math><mi>O</mi></math></span> can be viewed as a quantum analogue of BGG category <span><math><mi>O</mi></math></span>. We give a coherent model for its principal block at roots of unity, using the non-commutative Springer resolution defined by Bezrukavnikov–Mirković. In particular, the principal block is derived equivalent to the affine Hecke category. As an application, we endow the principal block with a canonical grading, and show that the graded multiplicity of simple module in Verma module is given by the generic Kazhdan–Lusztig polynomial.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"490 ","pages":"Article 110830"},"PeriodicalIF":1.5,"publicationDate":"2026-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-10DOI: 10.1016/j.aim.2026.110844
Inkang Kim , Pierre Pansu , Xueyuan Wan
We show that every integer in the interval is achieved by the signature of a rank 2p flat symplectic bundle over a surface with boundary Σ. When , one can prescribe the type (elliptic, parabolic, hyperbolic) of the holonomy along the boundary.
{"title":"On possible values of the signature of flat symplectic bundles over surfaces with boundary","authors":"Inkang Kim , Pierre Pansu , Xueyuan Wan","doi":"10.1016/j.aim.2026.110844","DOIUrl":"10.1016/j.aim.2026.110844","url":null,"abstract":"<div><div>We show that every integer in the interval <span><math><mo>[</mo><mn>2</mn><mi>p</mi><mi>χ</mi><mo>(</mo><mi>Σ</mi><mo>)</mo><mo>,</mo><mo>−</mo><mn>2</mn><mi>p</mi><mi>χ</mi><mo>(</mo><mi>Σ</mi><mo>)</mo><mo>]</mo></math></span> is achieved by the signature of a rank 2<em>p</em> flat symplectic bundle over a surface with boundary Σ. When <span><math><mi>p</mi><mo>=</mo><mn>1</mn></math></span>, one can prescribe the type (elliptic, parabolic, hyperbolic) of the holonomy along the boundary.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"490 ","pages":"Article 110844"},"PeriodicalIF":1.5,"publicationDate":"2026-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146170468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-04DOI: 10.1016/j.aim.2026.110841
Gautam Aishwarya , Liran Rotem
We study the connection between the concavity properties of a measure ν and the convexity properties of the associated relative entropy along optimal transport. As a corollary we prove a new dimensional Brunn–Minkowski inequality for centered star-shaped bodies, when the measure ν is log-concave with a p-homogeneous potential (such as the Gaussian measure). Our method allows us to go beyond the usual convexity assumption on the sets that is fundamentally essential for the standard differential-geometric technique in this area.
We then take a finer look at the convexity properties of the Gaussian relative entropy, which yields new functional inequalities. First we obtain curvature and dimensional reinforcements to Otto–Villani's HWI inequality in Gauss space, when restricted to even strongly log-concave measures. As corollaries, we obtain improved versions of Gross' Logarithmic Sobolev inequality and Talagrand's transportation cost inequality in this setting.
{"title":"New Brunn–Minkowski and functional inequalities via convexity of entropy","authors":"Gautam Aishwarya , Liran Rotem","doi":"10.1016/j.aim.2026.110841","DOIUrl":"10.1016/j.aim.2026.110841","url":null,"abstract":"<div><div>We study the connection between the concavity properties of a measure <em>ν</em> and the convexity properties of the associated relative entropy <span><math><mi>D</mi><mo>(</mo><mo>⋅</mo><mo>‖</mo><mi>ν</mi><mo>)</mo></math></span> along optimal transport. As a corollary we prove a new dimensional Brunn–Minkowski inequality for centered star-shaped bodies, when the measure <em>ν</em> is log-concave with a p-homogeneous potential (such as the Gaussian measure). Our method allows us to go beyond the usual convexity assumption on the sets that is fundamentally essential for the standard differential-geometric technique in this area.</div><div>We then take a finer look at the convexity properties of the Gaussian relative entropy, which yields new functional inequalities. First we obtain curvature and dimensional reinforcements to Otto–Villani's HWI inequality in Gauss space, when restricted to even strongly log-concave measures. As corollaries, we obtain improved versions of Gross' Logarithmic Sobolev inequality and Talagrand's transportation cost inequality in this setting.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"490 ","pages":"Article 110841"},"PeriodicalIF":1.5,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-04DOI: 10.1016/j.aim.2026.110819
Christopher J. Bishop , David L. Bishop
We strengthen the Weierstrass approximation theorem by proving that any real-valued continuous function on an interval can be uniformly approximated by a real-valued polynomial with only real critical points and whose derivatives converge to zero almost everywhere on I. Alternatively, the approximants may be chosen so that the derivatives converge to plus infinity almost everywhere, or so that these behaviors each occur almost everywhere on specified sets. This extends work by the second author, showing that the derivatives can also be taken to diverge pointwise almost everywhere. Together, these results prove that a 1994 theorem of Clunie and Kuijlaars is sharp.
{"title":"Approximation by singular polynomial sequences","authors":"Christopher J. Bishop , David L. Bishop","doi":"10.1016/j.aim.2026.110819","DOIUrl":"10.1016/j.aim.2026.110819","url":null,"abstract":"<div><div>We strengthen the Weierstrass approximation theorem by proving that any real-valued continuous function on an interval <span><math><mi>I</mi><mo>⊂</mo><mi>R</mi></math></span> can be uniformly approximated by a real-valued polynomial with only real critical points and whose derivatives converge to zero almost everywhere on <em>I</em>. Alternatively, the approximants may be chosen so that the derivatives converge to plus infinity almost everywhere, or so that these behaviors each occur almost everywhere on specified sets. This extends work by the second author, showing that the derivatives can also be taken to diverge pointwise almost everywhere. Together, these results prove that a 1994 theorem of Clunie and Kuijlaars is sharp.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"490 ","pages":"Article 110819"},"PeriodicalIF":1.5,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-04DOI: 10.1016/j.aim.2026.110798
William Graham, Scott Joseph Larson
We study the torus-equivariant cohomology of weighted flag varieties, and prove a positivity property in the equivariant cohomology and Chow groups of weighted flag varieties, analogous to the non-weighted positivity proved in [23]. Our result strengthens and generalizes the positivity proved for weighted Grassmannians by Abe-Matsumura [1]. The positivity property is expressed in terms of weighted roots, which are used to describe weights of torus equivariant curves in weighted flag varieties. This provides a geometric interpretation of the parameters used in [1]. We approach weighted flag varieties from a uniform Lie-theoretic point of view, providing a more general definition than has appeared previously, and prove other general results about weighted flag varieties in this setting, including a Borel presentation of the equivariant cohomology. In addition, we generalize some results obtained for weighted Grassmannians or more generally type A ([1], [6]); in particular, we obtain descriptions of restrictions to fixed points, the GKM description of the cohomology, and a weighted Chevalley formula.
{"title":"Positivity in weighted flag varieties","authors":"William Graham, Scott Joseph Larson","doi":"10.1016/j.aim.2026.110798","DOIUrl":"10.1016/j.aim.2026.110798","url":null,"abstract":"<div><div>We study the torus-equivariant cohomology of weighted flag varieties, and prove a positivity property in the equivariant cohomology and Chow groups of weighted flag varieties, analogous to the non-weighted positivity proved in <span><span>[23]</span></span>. Our result strengthens and generalizes the positivity proved for weighted Grassmannians by Abe-Matsumura <span><span>[1]</span></span>. The positivity property is expressed in terms of weighted roots, which are used to describe weights of torus equivariant curves in weighted flag varieties. This provides a geometric interpretation of the parameters used in <span><span>[1]</span></span>. We approach weighted flag varieties from a uniform Lie-theoretic point of view, providing a more general definition than has appeared previously, and prove other general results about weighted flag varieties in this setting, including a Borel presentation of the equivariant cohomology. In addition, we generalize some results obtained for weighted Grassmannians or more generally type <em>A</em> (<span><span>[1]</span></span>, <span><span>[6]</span></span>); in particular, we obtain descriptions of restrictions to fixed points, the GKM description of the cohomology, and a weighted Chevalley formula.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"489 ","pages":"Article 110798"},"PeriodicalIF":1.5,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-04DOI: 10.1016/j.aim.2026.110818
Marco Abate, Ian Short
We unify and advance a host of works on iterated function systems of holomorphic self-maps of hyperbolic Riemann surfaces. Our foremost result is a generalisation to left iterated function systems of an unpublished and little known theorem of Heins on iteration in the unit disc. Applications abound – to work of Benini et al. on transcendental dynamics, to the theory of hyperbolic steps of holomorphic maps, and to left semiconjugacy in the unit disc. We extend other work of Benini et al. and Ferreira on relatively compact left iterated function systems, and we prove a hyperbolic distance inequality for holomorphic maps that generalises a theorem of Bracci, Kraus, and Roth. Additionally, we strengthen results of the first author and Christodoulou on left iterated function systems, removing the need for Bloch domains, and we answer an open question from their work. Finally, we establish a version of the Heins theorem for right iterated functions systems, and we generalise theorems of Beardon and Kuznetsov on right iterated function systems in relatively compact semigroups of holomorphic maps.
我们统一并提出了关于双曲黎曼曲面全纯自映射的迭代函数系统的大量工作。我们最重要的结果是将Heins关于单位圆盘上迭代的一个尚未发表且鲜为人知的定理推广到左迭代函数系统。应用广泛- Benini等人在先验动力学上的工作，全纯映射的双曲阶理论，以及单位圆盘上的左半共轭。我们推广了Benini et al.和Ferreira在相对紧的左迭代函数系统上的其他工作，并证明了全纯映射的双曲距离不等式，推广了Bracci， Kraus和Roth的定理。此外，我们加强了第一作者和Christodoulou关于左迭代函数系统的结果，消除了对Bloch域的需要，并回答了他们工作中的一个开放问题。最后，我们建立了关于右迭代函数系统的Heins定理的一个版本，并推广了关于全纯映射的相对紧半群上的右迭代函数系统的Beardon定理和Kuznetsov定理。
{"title":"Iterated function systems of holomorphic maps","authors":"Marco Abate, Ian Short","doi":"10.1016/j.aim.2026.110818","DOIUrl":"10.1016/j.aim.2026.110818","url":null,"abstract":"<div><div>We unify and advance a host of works on iterated function systems of holomorphic self-maps of hyperbolic Riemann surfaces. Our foremost result is a generalisation to left iterated function systems of an unpublished and little known theorem of Heins on iteration in the unit disc. Applications abound – to work of Benini et al. on transcendental dynamics, to the theory of hyperbolic steps of holomorphic maps, and to left semiconjugacy in the unit disc. We extend other work of Benini et al. and Ferreira on relatively compact left iterated function systems, and we prove a hyperbolic distance inequality for holomorphic maps that generalises a theorem of Bracci, Kraus, and Roth. Additionally, we strengthen results of the first author and Christodoulou on left iterated function systems, removing the need for Bloch domains, and we answer an open question from their work. Finally, we establish a version of the Heins theorem for right iterated functions systems, and we generalise theorems of Beardon and Kuznetsov on right iterated function systems in relatively compact semigroups of holomorphic maps.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"490 ","pages":"Article 110818"},"PeriodicalIF":1.5,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-03DOI: 10.1016/j.aim.2026.110825
Florian Haberberger , Christian Hainzl , Benjamin Schlein , Arnaud Triay
We consider a Bose gas at density , interacting through a repulsive potential with scattering length . We prove an upper bound for the free energy of the system, valid at low temperature . Combined with the recent lower bound obtained in [18], our estimate resolves the free energy per unit volume up to and including the Lee–Huang–Yang order .
{"title":"Upper bound for the free energy of dilute Bose gases at low temperature","authors":"Florian Haberberger , Christian Hainzl , Benjamin Schlein , Arnaud Triay","doi":"10.1016/j.aim.2026.110825","DOIUrl":"10.1016/j.aim.2026.110825","url":null,"abstract":"<div><div>We consider a Bose gas at density <span><math><mi>ρ</mi><mo>></mo><mn>0</mn></math></span>, interacting through a repulsive potential <span><math><mi>V</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> with scattering length <span><math><mi>a</mi><mo>></mo><mn>0</mn></math></span>. We prove an upper bound for the free energy of the system, valid at low temperature <span><math><mi>T</mi><mo>≲</mo><mi>ρ</mi><mi>a</mi></math></span>. Combined with the recent lower bound obtained in <span><span>[18]</span></span>, our estimate resolves the free energy per unit volume up to and including the Lee–Huang–Yang order <span><math><mi>a</mi><msup><mrow><mi>ρ</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mo>(</mo><mi>ρ</mi><msup><mrow><mi>a</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"490 ","pages":"Article 110825"},"PeriodicalIF":1.5,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-03DOI: 10.1016/j.aim.2026.110824
James Hyde , Yash Lodha
A fundamental notion in group theory, which originates in an article of Ulam and von Neumann from 1947 is uniform simplicity. A group G is said to be n-uniformly simple for if for every , there is a product of no more than n conjugates of g and that equals f. Then G is uniformly simple if it is n-uniformly simple for some , and we refer to the smallest such n as the Ulam width, denoted as . If G is simple but not uniformly simple, one declares . In this article, we construct for each , a finitely presented infinite simple group G such that . These are the first such examples among the class of finitely presented infinite simple groups. For the class of finitely generated (but not finitely presentable) infinite simple groups, the existence of such examples was settled in the work of Muranov [21]. However, this had remained open for the class of finitely presented infinite simple groups. Our examples are also of type , which means that they are fundamental groups of aspherical CW complexes with finitely many cells in each dimension. Uniformly simple groups are in particular uniformly perfect: there is an such that every element of the group can be expressed as a product of at most n commutators of elements in the group. We also show that the analogous notion of width for uniform perfection is unbounded for our family of finitely presented infinite simple groups. To our knowledge, this is also the first such family.
{"title":"On Ulam widths of finitely presented infinite simple groups","authors":"James Hyde , Yash Lodha","doi":"10.1016/j.aim.2026.110824","DOIUrl":"10.1016/j.aim.2026.110824","url":null,"abstract":"<div><div>A fundamental notion in group theory, which originates in an article of Ulam and von Neumann from 1947 is <em>uniform simplicity</em>. A group <em>G</em> is said to be <em>n-uniformly simple</em> for <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span> if for every <span><math><mi>f</mi><mo>,</mo><mi>g</mi><mo>∈</mo><mi>G</mi><mo>∖</mo><mo>{</mo><mi>i</mi><mi>d</mi><mo>}</mo></math></span>, there is a product of no more than <em>n</em> conjugates of <em>g</em> and <span><math><msup><mrow><mi>g</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span> that equals <em>f</em>. Then <em>G</em> is <em>uniformly simple</em> if it is <em>n-uniformly simple</em> for some <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span>, and we refer to the smallest such <em>n</em> as the <em>Ulam width</em>, denoted as <span><math><mi>R</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. If <em>G</em> is simple but not uniformly simple, one declares <span><math><mi>R</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mo>∞</mo></math></span>. In this article, we construct for each <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span>, a finitely presented infinite simple group <em>G</em> such that <span><math><mi>n</mi><mo><</mo><mi>R</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo><</mo><mo>∞</mo></math></span>. These are the first such examples among the class of finitely presented infinite simple groups. For the class of finitely generated (but not finitely presentable) infinite simple groups, the existence of such examples was settled in the work of Muranov <span><span>[21]</span></span>. However, this had remained open for the class of finitely presented infinite simple groups. Our examples are also of type <span><math><msub><mrow><mi>F</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>, which means that they are fundamental groups of aspherical CW complexes with finitely many cells in each dimension. Uniformly simple groups are in particular <em>uniformly perfect</em>: there is an <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span> such that every element of the group can be expressed as a product of at most <em>n</em> commutators of elements in the group. We also show that the analogous notion of width for uniform perfection is unbounded for our family of finitely presented infinite simple groups. To our knowledge, this is also the first such family.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"490 ","pages":"Article 110824"},"PeriodicalIF":1.5,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-03DOI: 10.1016/j.aim.2026.110831
Frederik Benirschke, Carlos A. Serván
We correct a mistake in the proof of the main theorem of “Isometric embeddings of Teichmüller spaces are covering constructions.” Importantly, the results are unchanged.
{"title":"Erratum to “Isometric embeddings of Teichmüller spaces are covering constructions”","authors":"Frederik Benirschke, Carlos A. Serván","doi":"10.1016/j.aim.2026.110831","DOIUrl":"10.1016/j.aim.2026.110831","url":null,"abstract":"<div><div>We correct a mistake in the proof of the main theorem of “Isometric embeddings of Teichmüller spaces are covering constructions.” Importantly, the results are unchanged.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"489 ","pages":"Article 110831"},"PeriodicalIF":1.5,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-03DOI: 10.1016/j.aim.2026.110826
Emma Brakkee , Chiara Camere , Annalisa Grossi , Laura Pertusi , Giulia Saccà , Sasha Viktorova
Generalizing work of Markushevich–Tikhomirov and Arbarello–Saccà–Ferretti, we use relative Prym varieties to construct Lagrangian fibered symplectic varieties in infinitely many dimensions. We then give criteria for when the construction yields primitive symplectic varieties, respectively, irreducible symplectic varieties. The starting point of the construction is a K3 surface endowed with an anti-symplectic involution and an effective linear system on the quotient surface. We give sufficient conditions on the linear system to ensure that the relative Prym varieties satisfy the criteria above. As a consequence, we produce infinite series of irreducible symplectic varieties.
{"title":"Irreducible symplectic varieties via relative Prym varieties","authors":"Emma Brakkee , Chiara Camere , Annalisa Grossi , Laura Pertusi , Giulia Saccà , Sasha Viktorova","doi":"10.1016/j.aim.2026.110826","DOIUrl":"10.1016/j.aim.2026.110826","url":null,"abstract":"<div><div>Generalizing work of Markushevich–Tikhomirov and Arbarello–Saccà–Ferretti, we use relative Prym varieties to construct Lagrangian fibered symplectic varieties in infinitely many dimensions. We then give criteria for when the construction yields primitive symplectic varieties, respectively, irreducible symplectic varieties. The starting point of the construction is a <em>K</em>3 surface endowed with an anti-symplectic involution and an effective linear system on the quotient surface. We give sufficient conditions on the linear system to ensure that the relative Prym varieties satisfy the criteria above. As a consequence, we produce infinite series of irreducible symplectic varieties.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"490 ","pages":"Article 110826"},"PeriodicalIF":1.5,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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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