Forum of Mathematics Sigma最新文献_第2页

Cyclic coverings of genus curves of Sophie Germain type 索菲-日耳曼型属曲线的循环覆盖

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-05-21 DOI: 10.1017/fms.2024.42

J.C. Naranjo, A. Ortega, I. Spelta

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引用次数: 0

The Coble quadric 科布尔四边形

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-05-17 DOI: 10.1017/fms.2024.52

Vladimiro Benedetti, Michele Bolognesi, Daniele Faenzi, Laurent Manivel

{"title":"The Coble quadric","authors":"Vladimiro Benedetti, Michele Bolognesi, Daniele Faenzi, Laurent Manivel","doi":"10.1017/fms.2024.52","DOIUrl":"https://doi.org/10.1017/fms.2024.52","url":null,"abstract":"Given a smooth genus three curve <jats:italic>C</jats:italic>, the moduli space of rank two stable vector bundles on <jats:italic>C</jats:italic> with trivial determinant embeds in <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000525_inline1.png\"/> <jats:tex-math> ${mathbb {P}}^8$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> as a hypersurface whose singular locus is the Kummer threefold of <jats:italic>C</jats:italic>; this hypersurface is the Coble quartic. Gruson, Sam and Weyman realized that this quartic could be constructed from a general skew-symmetric four-form in eight variables. Using the lines contained in the quartic, we prove that a similar construction allows to recover <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000525_inline2.png\"/> <jats:tex-math> $operatorname {mathrm {SU}}_C(2,L)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, the moduli space of rank two stable vector bundles on <jats:italic>C</jats:italic> with fixed determinant of odd degree <jats:italic>L</jats:italic>, as a subvariety of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000525_inline3.png\"/> <jats:tex-math> $G(2,8)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. In fact, each point <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000525_inline4.png\"/> <jats:tex-math> $pin C$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> defines a natural embedding of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000525_inline5.png\"/> <jats:tex-math> $operatorname {mathrm {SU}}_C(2,{mathcal {O}}(p))$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> in <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000525_inline6.png\"/> <jats:tex-math> $G(2,8)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. We show that, for the generic such embedding, there exists a unique quadratic section of the Grassmannian which is singular exactly along the image of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2050509424000525_inline7.png\"/> <jats:tex-math> $operatorname {mathrm {SU}}_C(2,{mathcal {O}}(p))$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and thus deserves to be coined the Coble quadric of the pointed curve <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":"189 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141062871","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}

引用次数: 0

Adams’ cobar construction as a monoidal -coalgebra model of the based loop space 亚当斯的科巴结构是基于环空间的单项式-代数模型

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-05-15 DOI: 10.1017/fms.2024.50

Anibal M. Medina-Mardones, Manuel Rivera

引用次数: 0

Limit pretrees for free group automorphisms: existence 自由群自形化的极限预树：存在性

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-05-10 DOI: 10.1017/fms.2024.38

Jean Pierre Mutanguha

引用次数: 0

Minimal subdynamics and minimal flows without characteristic measures 无特征措施的最小亚动力学和最小流动

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-05-10 DOI: 10.1017/fms.2024.41

Joshua Frisch, Brandon Seward, Andy Zucker

{"title":"Minimal subdynamics and minimal flows without characteristic measures","authors":"Joshua Frisch, Brandon Seward, Andy Zucker","doi":"10.1017/fms.2024.41","DOIUrl":"https://doi.org/10.1017/fms.2024.41","url":null,"abstract":"Given a countable group G and a G-flow X, a probability measure $mu $ on X is called characteristic if it is $mathrm {Aut}(X, G)$ -invariant. Frisch and Tamuz asked about the existence of a minimal G-flow, for any group G, which does not admit a characteristic measure. We construct for every countable group G such a minimal flow. Along the way, we are motivated to consider a family of questions we refer to as minimal subdynamics: Given a countable group G and a collection of infinite subgroups ${Delta _i: iin I}$ , when is there a faithful G-flow for which every $Delta _i$ acts minimally?","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":"29 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930003","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}

引用次数: 0

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus 随机缝合两难的扩展及其在分数随机微积分中的应用

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-04-11 DOI: 10.1017/fms.2024.32

Toyomu Matsuda, Nicolas Perkowski

引用次数: 0

Generic Stability Independence and Treeless Theories 通用稳定性独立性和无树理论

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-04-08 DOI: 10.1017/fms.2024.35

Itay Kaplan, Nicholas Ramsey, Pierre Simon

引用次数: 0

Generic Beauville’s Conjecture 通用博维尔猜想

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-04-08 DOI: 10.1017/fms.2024.21

Izzet Coskun, Eric Larson, Isabel Vogt

{"title":"Generic Beauville’s Conjecture","authors":"Izzet Coskun, Eric Larson, Isabel Vogt","doi":"10.1017/fms.2024.21","DOIUrl":"https://doi.org/10.1017/fms.2024.21","url":null,"abstract":"Let $alpha colon X to Y$ be a finite cover of smooth curves. Beauville conjectured that the pushforward of a general vector bundle under $alpha $ is semistable if the genus of Y is at least $1$ and stable if the genus of Y is at least $2$ . We prove this conjecture if the map $alpha $ is general in any component of the Hurwitz space of covers of an arbitrary smooth curve Y.","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":"98 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578952","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}

引用次数: 0

A remark on Gibbs measures with log-correlated Gaussian fields 关于具有对数相关高斯场的吉布斯量纲的评论

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-04-08 DOI: 10.1017/fms.2024.28

Tadahiro Oh, Kihoon Seong, Leonardo Tolomeo

{"title":"A remark on Gibbs measures with log-correlated Gaussian fields","authors":"Tadahiro Oh, Kihoon Seong, Leonardo Tolomeo","doi":"10.1017/fms.2024.28","DOIUrl":"https://doi.org/10.1017/fms.2024.28","url":null,"abstract":"We study Gibbs measures with log-correlated base Gaussian fields on the d-dimensional torus. In the defocusing case, the construction of such Gibbs measures follows from Nelson’s argument. In this paper, we consider the focusing case with a quartic interaction. Using the variational formulation, we prove nonnormalizability of the Gibbs measure. When $d = 2$ , our argument provides an alternative proof of the nonnormalizability result for the focusing $Phi ^4_2$ -measure by Brydges and Slade (1996). Furthermore, we provide a precise rate of divergence, where the constant is characterized by the optimal constant for a certain Bernstein’s inequality on $mathbb R^d$ . We also go over the construction of the focusing Gibbs measure with a cubic interaction. In the appendices, we present (a) nonnormalizability of the Gibbs measure for the two-dimensional Zakharov system and (b) the construction of focusing quartic Gibbs measures with smoother base Gaussian measures, showing a critical nature of the log-correlated Gibbs measure with a focusing quartic interaction.","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":"96 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140579263","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}

引用次数: 0

Cohomological Descent for Faltings Ringed Topos 法尔廷斯环状拓扑的同源后裔

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-04-02 DOI: 10.1017/fms.2024.26

Tongmu He

引用次数: 0