Inventiones mathematicae最新文献_第2页

Reductive quotients of klt singularities klt 奇点的还原商

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-07-22 DOI: 10.1007/s00222-024-01280-2

Lukas Braun, Daniel Greb, Kevin Langlois, Joaquín Moraga

{"title":"Reductive quotients of klt singularities","authors":"Lukas Braun, Daniel Greb, Kevin Langlois, Joaquín Moraga","doi":"10.1007/s00222-024-01280-2","DOIUrl":"https://doi.org/10.1007/s00222-024-01280-2","url":null,"abstract":"We prove that the quotient of a klt type singularity by a reductive group is of klt type in characteristic 0. In particular, given a klt variety (X) endowed with the action of a reductive group (G) and admitting a quasi-projective good quotient (Xrightarrow X/!/G), we can find a boundary (B) on (X/!/G) so that the pair ((X/!/G,B)) is klt. This applies for example to GIT-quotients of klt varieties. Our main result has consequences for complex spaces obtained as quotients of Hamiltonian Kähler (G)-manifolds, for collapsings of homogeneous vector bundles as introduced by Kempf, and for good moduli spaces of smooth Artin stacks. In particular, it implies that the good moduli space parametrizing (n)-dimensional K-polystable smooth Fano varieties of volume (v) has klt type singularities. As a corresponding result regarding global geometry, we show that quotients of Mori Dream Spaces with klt Cox rings are Mori Dream Spaces with klt Cox ring. This in turn applies to show that projective GIT-quotients of varieties of Fano type are of Fano type; in particular, projective moduli spaces of semistable quiver representations are of Fano type.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"69 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141739640","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: 0

Direct summands of klt singularities klt 奇点的直接求和

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-07-22 DOI: 10.1007/s00222-024-01281-1

Ziquan Zhuang

引用次数: 0

Stationary measures for integrable polymers on a strip 条带上可积分聚合物的静态量纲

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-06-25 DOI: 10.1007/s00222-024-01277-x

Guillaume Barraquand, Ivan Corwin, Zongrui Yang

引用次数: 0

A diagram-free approach to the stochastic estimates in regularity structures 正则结构中随机估计的无图方法

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-06-14 DOI: 10.1007/s00222-024-01275-z

Pablo Linares, Felix Otto, Markus Tempelmayr, Pavlos Tsatsoulis

{"title":"A diagram-free approach to the stochastic estimates in regularity structures","authors":"Pablo Linares, Felix Otto, Markus Tempelmayr, Pavlos Tsatsoulis","doi":"10.1007/s00222-024-01275-z","DOIUrl":"https://doi.org/10.1007/s00222-024-01275-z","url":null,"abstract":"In this paper, we explore the version of Hairer’s regularity structures based on a greedier index set than trees, as introduced in (Otto et al. in A priori bounds for quasi-linear SPDEs in the full sub-critical regime, 2021, arXiv:2103.11039) and algebraically characterized in (Linares et al. in Comm. Am. Math. Soc. 3:1–64, 2023). More precisely, we construct and stochastically estimate the renormalized model postulated in (Otto et al. in A priori bounds for quasi-linear SPDEs in the full sub-critical regime, 2021, arXiv:2103.11039), avoiding the use of Feynman diagrams but still in a fully automated, i. e. inductive way. This is carried out for a class of quasi-linear parabolic PDEs driven by noise in the full singular but renormalizable range. We assume a spectral gap inequality on the (not necessarily Gaussian) noise ensemble. The resulting control on the variance of the model naturally complements its vanishing expectation arising from the BPHZ-choice of renormalization. We capture the gain in regularity on the level of the Malliavin derivative of the model by describing it as a modelled distribution. Symmetry is an important guiding principle and built-in on the level of the renormalization Ansatz. Our approach is analytic and top-down rather than combinatorial and bottom-up.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"110 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507898","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: 0

The geometry of maximal development and shock formation for the Euler equations in multiple space dimensions 欧拉方程在多空间维度上的最大发展和冲击形成的几何形状

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-06-03 DOI: 10.1007/s00222-024-01269-x

Steve Shkoller, Vlad Vicol

{"title":"The geometry of maximal development and shock formation for the Euler equations in multiple space dimensions","authors":"Steve Shkoller, Vlad Vicol","doi":"10.1007/s00222-024-01269-x","DOIUrl":"https://doi.org/10.1007/s00222-024-01269-x","url":null,"abstract":"We construct a fundamental piece of the boundary of the maximal globally hyperbolic development (MGHD) of Cauchy data for the multi-dimensional compressible Euler equations, which is necessary for the local shock development problem. For an open set of compressive and generic (H^{7}) initial data, we construct unique (H^{7}) solutions to the Euler equations in the maximal spacetime region below a given time-slice, beyond the time of the first singularity; at any point in this spacetime, the solution can be smoothly and uniquely computed by tracing both the fast and slow acoustic characteristic surfaces backward-in-time, until reaching the Cauchy data prescribed along the initial time-slice. The future temporal boundary of this spacetime region is a singular hypersurface, containing the union of three sets: first, a co-dimension-2 surface of “first singularities” called the pre-shock; second, a downstream hypersurface called the singular set emanating from the pre-shock, on which the Euler solution experiences a continuum of gradient catastrophes; third, an upstream hypersurface consisting of a Cauchy horizon emanating from the pre-shock, which the Euler solution cannot reach. We develop a new geometric framework for the description of the acoustic characteristic surfaces which is based on the Arbitrary Lagrangian Eulerian (ALE) framework, and combine this with a new type of differentiated Riemann variables which are linear combinations of gradients of velocity, sound speed, and the curvature of the fast acoustic characteristic surfaces. With these new variables, we establish uniform (H^{7}) Sobolev bounds for solutions to the Euler equations without derivative loss and with optimal regularity.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"103 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141258348","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: 0

Moments of quadratic twists of modular $L$ -functions 模态 $L$ 函数的二次扭曲力矩

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-05-31 DOI: 10.1007/s00222-024-01265-1

Xiannan Li

引用次数: 0

On the largest product-free subsets of the alternating groups 关于交替群的最大无积子集

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-05-29 DOI: 10.1007/s00222-024-01273-1

Peter Keevash, Noam Lifshitz, Dor Minzer

{"title":"On the largest product-free subsets of the alternating groups","authors":"Peter Keevash, Noam Lifshitz, Dor Minzer","doi":"10.1007/s00222-024-01273-1","DOIUrl":"https://doi.org/10.1007/s00222-024-01273-1","url":null,"abstract":"A subset (A) of a group (G) is called product-free if there is no solution to (a=bc) with (a,b,c) all in (A). It is easy to see that the largest product-free subset of the symmetric group (S_{n}) is obtained by taking the set of all odd permutations, i.e. (S_{n} backslash A_{n}), where (A_{n}) is the alternating group. In 1985 Babai and Sós (Eur. J. Comb. 6(2):101–114, 1985) conjectured that the group (A_{n}) also contains a product-free set of constant density. This conjecture was refuted by Gowers (whose result was subsequently improved by Eberhard), still leaving the long-standing problem of determining the largest product-free subset of (A_{n}) wide open. We solve this problem for large (n), showing that the maximum size is achieved by the previously conjectured extremal examples, namely families of the form (left { pi :,pi (x)in I, pi (I)cap I=varnothing right } ) and their inverses. Moreover, we show that the maximum size is only achieved by these extremal examples, and we have stability: any product-free subset of (A_{n}) of nearly maximum size is structurally close to an extremal example. Our proof uses a combination of tools from Combinatorics and Non-abelian Fourier Analysis, including a crucial new ingredient exploiting some recent theory developed by Filmus, Kindler, Lifshitz and Minzer for global hypercontractivity on the symmetric group.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"63 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141167494","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: 0

Asymptotic stability of small standing solitary waves of the one-dimensional cubic-quintic Schrödinger equation 一维立方-五次方薛定谔方程的小驻留孤波的渐近稳定性

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-05-28 DOI: 10.1007/s00222-024-01270-4

Yvan Martel

引用次数: 0

A Lagrangian filling for every cluster seed 每个集群种子的拉格朗日填充

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-05-27 DOI: 10.1007/s00222-024-01268-y

Roger Casals, Honghao Gao

引用次数: 0

Isotropic and numerical equivalence for Chow groups and Morava K-theories 周群和莫拉瓦 K 理论的等价性和数值等价性