Compositio Mathematica最新文献_第6页

Approximation and homotopy in regulous geometry 正则几何中的近似与同伦

1区数学

Compositio Mathematica Pub Date : 2023-11-09 DOI: 10.1112/s0010437x23007522

Wojciech Kucharz

引用次数: 0

On equivariant topological modular forms 关于等变拓扑模形式

1区数学

Compositio Mathematica Pub Date : 2023-11-06 DOI: 10.1112/s0010437x23007509

David Gepner, Lennart Meier

引用次数: 20

Locality of relative symplectic cohomology for complete embeddings 完备嵌入的相对辛上同的局部性

1区数学

Compositio Mathematica Pub Date : 2023-10-10 DOI: 10.1112/s0010437x23007492

Yoel Groman, Umut Varolgunes

引用次数: 8

COM volume 159 issue 11 Cover and Front matter COM第159卷第11期封面和封面

1区数学

Compositio Mathematica Pub Date : 2023-10-09 DOI: 10.1112/s0010437x22008144

引用次数: 0

COM volume 159 issue 11 Cover and Back matter COM第159卷第11期封面和封底

1区数学

Compositio Mathematica Pub Date : 2023-10-09 DOI: 10.1112/s0010437x22008156

引用次数: 0

Generic Torelli and local Schottky theorems for Jacobian elliptic surfaces 雅可比椭圆曲面的一般Torelli定理和局部Schottky定理

1区数学

Compositio Mathematica Pub Date : 2023-10-06 DOI: 10.1112/s0010437x23007443

N. I. Shepherd-Barron

{"title":"Generic Torelli and local Schottky theorems for Jacobian elliptic surfaces","authors":"N. I. Shepherd-Barron","doi":"10.1112/s0010437x23007443","DOIUrl":"https://doi.org/10.1112/s0010437x23007443","url":null,"abstract":"Suppose that $f:Xto C$ is a general Jacobian elliptic surface over ${mathbb {C}}$ of irregularity $q$ and positive geometric genus $h$ . Assume that $10 h>12(q-1)$ , that $h>0$ and let $overline {mathcal {E}ell ell }$ denote the stack of generalized elliptic curves. (1) The moduli stack $mathcal {JE}$ of such surfaces is smooth at the point $X$ and its tangent space $T$ there is naturally a direct sum of lines $(v_a)_{ain Z}$ , where $Zsubset C$ is the ramification locus of the classifying morphism $phi :Cto overline {mathcal {E}ell ell }$ that corresponds to $Xto C$ . (2) For each $ain Z$ the map $overline {nabla }_{v_a}:H^{2,0}(X)to H^{1,1}_{rm prim}(X)$ defined by the derivative $per_*$ of the period map $per$ is of rank one. Its image is a line ${mathbb {C}}[eta _a]$ and its kernel is $H^0(X,Omega ^2_X(-E_a))$ , where $E_a=f^{-1}(a)$ . (3) The classes $[eta _a]$ form an orthogonal basis of $H^{1,1}_{rm prim}(X)$ and $[eta _a]$ is represented by a meromorphic $2$ -form $eta _a$ in $H^0(X,Omega ^2_X(2E_a))$ of the second kind. (4) We prove a local Schottky theorem; that is, we give a description of $per_*$ in terms of a certain additional structure on the vector bundles that are involved. Assume further that $8h>10(q-1)$ and that $hge q+3$ . (5) Given the period point $per(X)$ of $X$ that classifies the Hodge structure on the primitive cohomology $H^2_{rm prim}(X)$ and the image of $T$ under $per_*$ we recover $Z$ as a subset of ${mathbb {P}}^{h-1}$ and then, by quadratic interpolation, the curve $C$ . (6) We prove a generic Torelli theorem for these surfaces. Everything relies on the construction, via certain kinds of Schiffer variations of curves, of certain variations of $X$ for which $per_*$ can be calculated. (In an earlier version of this paper we used variations constructed by Fay. However, Schiffer variations are slightly more powerful.)","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135351181","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}

引用次数: 5

On distributivity in higher algebra I: the universal property of bispans 高等代数中的分配律I:双盘的通用性

1区数学

Compositio Mathematica Pub Date : 2023-09-18 DOI: 10.1112/s0010437x23007388

Elden Elmanto, Rune Haugseng

{"title":"On distributivity in higher algebra I: the universal property of bispans","authors":"Elden Elmanto, Rune Haugseng","doi":"10.1112/s0010437x23007388","DOIUrl":"https://doi.org/10.1112/s0010437x23007388","url":null,"abstract":"Structures where we have both a contravariant (pullback) and a covariant (pushforward) functoriality that satisfy base change can be encoded by functors out of ( $infty$ -)categories of spans (or correspondences). In this paper, we study the more complicated setup where we have two pushforwards (an ‘additive’ and a ‘multiplicative’ one), satisfying a distributivity relation. Such structures can be described in terms of bispans (or polynomial diagrams). We show that there exist $(infty,2)$ -categories of bispans, characterized by a universal property: they corepresent functors out of $infty$ -categories of spans where the pullbacks have left adjoints and certain canonical 2-morphisms (encoding base change and distributivity) are invertible. This gives a universal way to obtain functors from bispans, which amounts to upgrading ‘monoid-like’ structures to ‘ring-like’ ones. For example, symmetric monoidal $infty$ -categories can be described as product-preserving functors from spans of finite sets, and if the tensor product is compatible with finite coproducts our universal property gives the canonical semiring structure using the coproduct and tensor product. More interestingly, we encode the additive and multiplicative transfers on equivariant spectra as a functor from bispans in finite $G$ -sets, extend the norms for finite étale maps in motivic spectra to a functor from certain bispans in schemes, and make $mathrm {Perf}(X)$ for $X$ a spectral Deligne–Mumford stack a functor of bispans using a multiplicative pushforward for finite étale maps in addition to the usual pullback and pushforward maps. Combining this with the polynomial functoriality of $K$ -theory constructed by Barwick, Glasman, Mathew, and Nikolaus, we obtain norms on algebraic $K$ -theory spectra.","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135109327","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}

引用次数: 5

Hamiltonian knottedness and lifting paths from the shape invariant 哈密顿结性和形状不变量的提升路径

1区数学

Compositio Mathematica Pub Date : 2023-09-18 DOI: 10.1112/s0010437x23007479

Richard Hind, Jun Zhang

引用次数: 0

On the étale cohomology of Hilbert modular varieties with torsion coefficients 带扭转系数的Hilbert模变体的<s:1>上同调性

1区数学

Compositio Mathematica Pub Date : 2023-09-18 DOI: 10.1112/s0010437x23007431

Ana Caraiani, Matteo Tamiozzo

引用次数: 4

Lagrangian configurations and Hamiltonian maps 拉格朗日构型和哈密顿映射