Transactions of the London Mathematical Society最新文献_第2页

Positive solutions for the fractional Schrödinger equations with logarithmic and critical non‐linearities 具有对数和临界非线性的分数阶Schrödinger方程的正解

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Transactions of the London Mathematical Society Pub Date : 2021-02-27 DOI: 10.1112/tlm3.12034

H. Fan, Zhaosheng Feng, Xingjie Yan

引用次数: 3

Homological and combinatorial aspects of virtually Cohen–Macaulay sheaves Cohen–Macaulay槽轮的同调和组合方面

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Transactions of the London Mathematical Society Pub Date : 2020-12-28 DOI: 10.1112/tlm3.12036

C. Berkesch, Patricia Klein, Michael C. Loper, J. Yang

{"title":"Homological and combinatorial aspects of virtually Cohen–Macaulay sheaves","authors":"C. Berkesch, Patricia Klein, Michael C. Loper, J. Yang","doi":"10.1112/tlm3.12036","DOIUrl":"https://doi.org/10.1112/tlm3.12036","url":null,"abstract":"When studying a graded module M over the Cox ring of a smooth projective toric variety X , there are two standard types of resolutions commonly used to glean information: free resolutions of M and vector bundle resolutions of its sheafification. Each approach comes with its own challenges. There is geometric information that free resolutions fail to encode, while vector bundle resolutions can resist study using algebraic and combinatorial techniques. Recently, Berkesch, Erman and Smith introduced virtual resolutions, which capture desirable geometric information and are also amenable to algebraic and combinatorial study. The theory of virtual resolutions includes a notion of a virtually Cohen–Macaulay property, though tools for assessing which modules are virtually Cohen–Macaulay have only recently started to be developed. In this article, we continue this research program in two related ways. The first is that, when X is a product of projective spaces, we produce a large new class of virtually Cohen–Macaulay Stanley–Reisner rings, which we show to be virtually Cohen–Macaulay via explicit constructions of appropriate virtual resolutions reflecting the underlying combinatorial structure. The second is that, for an arbitrary smooth projective toric variety X , we develop homological tools for assessing the virtual Cohen–Macaulay property. Some of these tools give exclusionary criteria, and others are constructive methods for producing suitably short virtual resolutions. We also use these tools to establish relationships among the arithmetically, geometrically and virtually Cohen–Macaulay properties.","PeriodicalId":41208,"journal":{"name":"Transactions of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47649399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 16

Counting curves on orbifolds 轨道上的曲线计数

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Transactions of the London Mathematical Society Pub Date : 2020-12-27 DOI: 10.1112/tlm3.12043

V. Erlandsson, J. Souto

引用次数: 2

Correlations in totally symmetric self‐complementary plane partitions 完全对称自互补平面分区中的相关关系

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Transactions of the London Mathematical Society Pub Date : 2020-12-23 DOI: 10.1112/tlm3.12039

Arvind Ayyer, S. Chhita

引用次数: 1

Gysin sequences and SU(2) ‐symmetries of C∗ ‐algebras Gysin序列与C*-代数的SU（2）对称性

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Transactions of the London Mathematical Society Pub Date : 2020-12-21 DOI: 10.1112/tlm3.12038

F. Arici, Jens Kaad

引用次数: 7

Issue Information 问题信息

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Transactions of the London Mathematical Society Pub Date : 2020-12-01 DOI: 10.1112/tlm3.12017

引用次数: 0

Twisted Eisenstein series, cotangent‐zeta sums, and quantum modular forms 扭曲的艾森斯坦级数、余切和和量子模形式

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Transactions of the London Mathematical Society Pub Date : 2020-09-28 DOI: 10.1112/tlm3.12022

A. Folsom

引用次数: 1

Finite groups, minimal bases and the intersection number 有限群，最小基和交点数

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Transactions of the London Mathematical Society Pub Date : 2020-09-21 DOI: 10.1112/tlm3.12040

Timothy C. Burness, Martino Garonzi, A. Lucchini

{"title":"Finite groups, minimal bases and the intersection number","authors":"Timothy C. Burness, Martino Garonzi, A. Lucchini","doi":"10.1112/tlm3.12040","DOIUrl":"https://doi.org/10.1112/tlm3.12040","url":null,"abstract":"Let G$G$ be a finite group and recall that the Frattini subgroup Frat(G)${rm Frat}(G)$ is the intersection of all the maximal subgroups of G$G$ . In this paper, we investigate the intersection number of G$G$ , denoted α(G)$alpha (G)$ , which is the minimal number of maximal subgroups whose intersection coincides with Frat(G)${rm Frat}(G)$ . In earlier work, we studied α(G)$alpha (G)$ in the special case where G$G$ is simple and here we extend the analysis to almost simple groups. In particular, we prove that α(G)⩽4$alpha (G) leqslant 4$ for every almost simple group G$G$ , which is best possible. We also establish new results on the intersection number of arbitrary finite groups, obtaining upper bounds that are defined in terms of the chief factors of the group. Finally, for almost simple groups G$G$ we present best possible bounds on a related invariant β(G)$beta (G)$ , which we call the base number of G$G$ . In this setting, β(G)$beta (G)$ is the minimal base size of G$G$ as we range over all faithful primitive actions of the group and we prove that the bound β(G)⩽4$beta (G) leqslant 4$ is optimal. Along the way, we study bases for the primitive action of the symmetric group Sab$S_{ab}$ on the set of partitions of [1,ab]$[1,ab]$ into a$a$ parts of size b$b$ , determining the exact base size for a⩾b$a geqslant b$ . This extends earlier work of Benbenishty, Cohen and Niemeyer.","PeriodicalId":41208,"journal":{"name":"Transactions of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45488388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

Completions of discrete cluster categories of type A A型离散聚类范畴的完备度

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Transactions of the London Mathematical Society Pub Date : 2020-06-12 DOI: 10.1112/tlm3.12025

Charles Paquette, Emine Yildirim

引用次数: 6

Exterior products of operators and superoptimal analytic approximation 算子的外积与超最优解析逼近

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Transactions of the London Mathematical Society Pub Date : 2020-04-14 DOI: 10.1112/tlm3.12035

Dimitrios Chiotis, Z. Lykova, Nicholas Young

引用次数: 1