Forum of Mathematics Sigma最新文献_第2页

Globally F-regular type of the moduli spaces of parabolic symplectic/orthogonal bundles on curves 曲线上抛物线交映/正交束的模空间的全局 F 不规则类型

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-05-27 DOI: 10.1017/fms.2024.57

Jianping Wang, Xueqing Wen

引用次数: 0

Strict positivity of Kähler–Einstein currents 凯勒-爱因斯坦电流的严格正向性

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-05-27 DOI: 10.1017/fms.2024.54

Vincent Guedj, Henri Guenancia, Ahmed Zeriahi

{"title":"Strict positivity of Kähler–Einstein currents","authors":"Vincent Guedj, Henri Guenancia, Ahmed Zeriahi","doi":"10.1017/fms.2024.54","DOIUrl":"https://doi.org/10.1017/fms.2024.54","url":null,"abstract":"Kähler–Einstein currents, also known as singular Kähler–Einstein metrics, have been introduced and constructed a little over a decade ago. These currents live on mildly singular compact Kähler spaces X and their two defining properties are the following: They are genuine Kähler–Einstein metrics on $X_{mathrm {reg}}$ , and they admit local bounded potentials near the singularities of X. In this note, we show that these currents dominate a Kähler form near the singular locus, when either X admits a global smoothing, or when X has isolated smoothable singularities. Our results apply to klt pairs and allow us to show that if X is any compact Kähler space of dimension three with log terminal singularities, then any singular Kähler–Einstein metric of nonpositive curvature dominates a Kähler form.","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170674","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

On the weight zero compactly supported cohomology of 关于权重为零的紧凑支撑同调的

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-05-27 DOI: 10.1017/fms.2024.53

Madeline Brandt, Melody Chan, Siddarth Kannan

{"title":"On the weight zero compactly supported cohomology of","authors":"Madeline Brandt, Melody Chan, Siddarth Kannan","doi":"10.1017/fms.2024.53","DOIUrl":"https://doi.org/10.1017/fms.2024.53","url":null,"abstract":"For $gge 2$ and $nge 0$ , let $mathcal {H}_{g,n}subset mathcal {M}_{g,n}$ denote the complex moduli stack of n-marked smooth hyperelliptic curves of genus g. A normal crossings compactification of this space is provided by the theory of pointed admissible $mathbb {Z}/2mathbb {Z}$ -covers. We explicitly determine the resulting dual complex, and we use this to define a graph complex which computes the weight zero compactly supported cohomology of $mathcal {H}_{g, n}$ . Using this graph complex, we give a sum-over-graphs formula for the $S_n$ -equivariant weight zero compactly supported Euler characteristic of $mathcal {H}_{g, n}$ . This formula allows for the computer-aided calculation, for each $gle 7$ , of the generating function $mathsf {h}_g$ </jats:alternativ","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141167644","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

Orthogonality relations for deep level Deligne–Lusztig schemes of Coxeter type Coxeter 型深层次 Deligne-Lusztig 方案的正交关系

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-05-22 DOI: 10.1017/fms.2024.55

Olivier Dudas, Alexander B. Ivanov

引用次数: 0

On divisorial stability of finite covers 论有限封面的分裂稳定性

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-05-22 DOI: 10.1017/fms.2024.47

Ruadhaí Dervan, Theodoros Stylianos Papazachariou

引用次数: 0

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

{"title":"Cyclic coverings of genus curves of Sophie Germain type","authors":"J.C. Naranjo, A. Ortega, I. Spelta","doi":"10.1017/fms.2024.42","DOIUrl":"https://doi.org/10.1017/fms.2024.42","url":null,"abstract":"We consider cyclic unramified coverings of degree d of irreducible complex smooth genus $2$ curves and their corresponding Prym varieties. They provide natural examples of polarized abelian varieties with automorphisms of order d. The rich geometry of the associated Prym map has been studied in several papers, and the cases $d=2, 3, 5, 7$ are quite well understood. Nevertheless, very little is known for higher values of d. In this paper, we investigate whether the covering can be reconstructed from its Prym variety, that is, whether the generic Prym Torelli theorem holds for these coverings. We prove this is so for the so-called Sophie Germain prime numbers, that is, for $dge 11$ prime such that $frac {d-1}2$ is also prime. We use results of arithmetic nature on $GL_2$ -type abelian varieties combined with theta-duality techniques.","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146863","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

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 C, the moduli space of rank two stable vector bundles on C with trivial determinant embeds in ${mathbb {P}}^8$ as a hypersurface whose singular locus is the Kummer threefold of C; 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 $operatorname {mathrm {SU}}_C(2,L)$ , the moduli space of rank two stable vector bundles on C with fixed determinant of odd degree L, as a subvariety of $G(2,8)$ . In fact, each point $pin C$ defines a natural embedding of $operatorname {mathrm {SU}}_C(2,{mathcal {O}}(p))$ in $G(2,8)$ . 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 $operatorname {mathrm {SU}}_C(2,{mathcal {O}}(p))$ and thus deserves to be coined the Coble quadric of the pointed curve <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"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

Quasimaps to moduli spaces of sheaves on a surface 曲面上的模空间准映射

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-05-17 DOI: 10.1017/fms.2024.48

Denis Nesterov

{"title":"Quasimaps to moduli spaces of sheaves on a surface","authors":"Denis Nesterov","doi":"10.1017/fms.2024.48","DOIUrl":"https://doi.org/10.1017/fms.2024.48","url":null,"abstract":"In this article, we study quasimaps to moduli spaces of sheaves on a $K3$ surface S. We construct a surjective cosection of the obstruction theory of moduli spaces of $epsilon $ -stable quasimaps. We then establish reduced wall-crossing formulas which relate the reduced Gromov–Witten theory of moduli spaces of sheaves on S and the reduced Donaldson–Thomas theory of $Stimes C$ , where C is a nodal curve. As applications, we prove the Hilbert-schemes part of the Igusa cusp form conjecture; higher-rank/rank-one Donaldson–Thomas correspondence with relative insertions on $Stimes C$ , if $g(C)leq 1$ ; Donaldson–Thomas/Pandharipande–Thomas correspondence with relative insertions on $Stimes mathbb {P}^1$ .","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141062604","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