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Categorical vs Topological Entropy of Autoequivalences of Surfaces 曲面自等价的分类熵与拓扑熵
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2019-09-06 DOI: 10.17323/1609-4514-2021-21-2-401-412
Dominique Mattei
{"title":"Categorical vs Topological Entropy of Autoequivalences of Surfaces","authors":"Dominique Mattei","doi":"10.17323/1609-4514-2021-21-2-401-412","DOIUrl":"https://doi.org/10.17323/1609-4514-2021-21-2-401-412","url":null,"abstract":"In this paper, we give an example of an autoequivalence with positive categorical entropy (in the sense of Dimitrov, Haiden, Katzarkov and Kontsevich) for any surface containing a (-2)-curve. Then we show that this equivalence gives another counter-example to a conjecture proposed by Kikuta and Takahashi. In a second part, we study the action on cohomology induced by spherical twists composed with standard autoequivalences on a surface S and show that their spectral radii correspond to the topological entropy of the corresponding automorphisms of S.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44056340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 8
Transition Polynomial as a Weight System for Binary Delta-Matroids 二元三角拟阵的过渡多项式权系统
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2019-07-08 DOI: 10.17323/1609-4514-2022-22-1-69-81
Alexander Dunaykin, V. Zhukov
{"title":"Transition Polynomial as a Weight System for Binary Delta-Matroids","authors":"Alexander Dunaykin, V. Zhukov","doi":"10.17323/1609-4514-2022-22-1-69-81","DOIUrl":"https://doi.org/10.17323/1609-4514-2022-22-1-69-81","url":null,"abstract":"To a singular knot K with n double points, one can associate a chord diagram with n chords. A chord diagram can also be understood as a 4-regular graph endowed with an oriented Euler circuit. For a given 4-regular graph, we can build a transition polynomial. We specialize this polynomial to a multiplicative weight system, that is, a function on chord diagrams satisfying 4-term relations and determining thus a knot invariant. We extend our function to ribbon graphs and further to binary delta-matroids and show that 4-term relations are satisfied for it.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42900074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3
The Boundary of the Orbital Beta Process 轨道贝塔过程的边界
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2019-05-21 DOI: 10.17323/1609-4514-2021-21-4-659-694
T. Assiotis, J. Najnudel
{"title":"The Boundary of the Orbital Beta Process","authors":"T. Assiotis, J. Najnudel","doi":"10.17323/1609-4514-2021-21-4-659-694","DOIUrl":"https://doi.org/10.17323/1609-4514-2021-21-4-659-694","url":null,"abstract":"The unitarily invariant probability measures on infinite Hermitian matrices have been classified by Pickrell, and by Olshanski and Vershik. This classification is equivalent to determining the boundary of a certain inhomogeneous Markov chain with given transition probabilities. This formulation of the problem makes sense for general $beta$-ensembles when one takes as the transition probabilities the Dixon-Anderson conditional probability distribution. In this paper we determine the boundary of this Markov chain for any $beta in (0,infty]$, also giving in this way a new proof of the classical $beta=2$ case. Finally, as a by-product of our results we obtain alternative proofs of the almost sure convergence of the rescaled Hua-Pickrell and Laguerre $beta$-ensembles to the general $beta$ Hua-Pickrell and $beta$ Bessel point processes respectively.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44121323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 16
Yulij Ilyashenko is 75 Yulij Ilyashenko享年75岁
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2019-05-13 DOI: 10.17323/1609-4514-2019-19-2-185-188
{"title":"Yulij Ilyashenko is 75","authors":"","doi":"10.17323/1609-4514-2019-19-2-185-188","DOIUrl":"https://doi.org/10.17323/1609-4514-2019-19-2-185-188","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42748977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Quasi-Periodic Kicking of Circle Diffeomorphisms Having Unique Fixed Points 具有唯一不动点的圆微分同态的拟周期踢脚
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2019-05-13 DOI: 10.17323/1609-4514-2019-19-2-189-216
Kristian Bjerklöv
{"title":"Quasi-Periodic Kicking of Circle Diffeomorphisms Having Unique Fixed Points","authors":"Kristian Bjerklöv","doi":"10.17323/1609-4514-2019-19-2-189-216","DOIUrl":"https://doi.org/10.17323/1609-4514-2019-19-2-189-216","url":null,"abstract":"We investigate the dynamics of certain homeomorphisms F: T-2 -> T-2 of the form F(x, y) = (x + omega , h(x)+ f (y)), where omega is an element of RQ, f: T -> T is a circle diffeomorphism wit ...","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42587700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Generalized Connections, Spinors, and Integrability of Generalized Structures on Courant Algebroids Courant代数群上的广义连接、旋量和广义结构的可积性
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2019-05-06 DOI: 10.17323/1609-4514-2021-21-4-695-736
V. Cort'es, L. David
{"title":"Generalized Connections, Spinors, and Integrability of Generalized Structures on Courant Algebroids","authors":"V. Cort'es, L. David","doi":"10.17323/1609-4514-2021-21-4-695-736","DOIUrl":"https://doi.org/10.17323/1609-4514-2021-21-4-695-736","url":null,"abstract":"We present a characterization, in terms of torsion-free generalized connections, for the integrability of various generalized structures (generalized almost complex structures, generalized almost hypercomplex structures, generalized almost Hermitian structures and generalized almost hyper-Hermitian structures) defined on Courant algebroids. We develop a new, self-contained, approach for the theory of Dirac generating operators for regular Courant algebroids. As an application we provide a criterion for the integrability of generalized almost Hermitian structures and generalized almost hyper-Hermitian structures defined on a regular Courant algebroid E, in terms of canonically defined differential operators on spinor bundles associated to E.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41985351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 7
On the Top Homology Group of the Johnson Kernel 关于Johnson核的上同调群
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2019-03-09 DOI: 10.17323/1609-4514-2022-22-1-83-102
A. Gaifullin
{"title":"On the Top Homology Group of the Johnson Kernel","authors":"A. Gaifullin","doi":"10.17323/1609-4514-2022-22-1-83-102","DOIUrl":"https://doi.org/10.17323/1609-4514-2022-22-1-83-102","url":null,"abstract":"The action of the mapping class group $mathrm{Mod}_g$ of an oriented surface $Sigma_g$ on the lower central series of $pi_1(Sigma_g)$ defines the descending filtration in $mathrm{Mod}_g$ called the Johnson filtration. The first two terms of it are the Torelli group $mathcal{I}_g$ and the Johnson kernel $mathcal{K}_g$. By a fundamental result of Johnson (1985), $mathcal{K}_g$ is the subgroup of $mathrm{Mod}_g$ generated by all Dehn twists about separating curves. In 2007, Bestvina, Bux, and Margalit showed the group $mathcal{K}_g$ has cohomological dimension $2g-3$. We prove that the top homology group $H_{2g-3}(mathcal{K}_g)$ is not finitely generated. In fact, we show that it contains a free abelian subgroup of infinite rank, hence, the vector space $H_{2g-3}(mathcal{K}_g,mathbb{Q})$ is infinite-dimensional. Moreover, we prove that $H_{2g-3}(mathcal{K}_g,mathbb{Q})$ is not finitely generated as a module over the group ring $mathbb{Q}[mathcal{I}_g]$.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46345034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3
Deformations of Polystable Sheaves on Surfaces: Quadraticity Implies Formality 曲面上聚稳定轴的变形:二次性意味着形式
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2019-02-18 DOI: 10.17323/1609-4514-2022-22-2-239-263
R. Bandiera, M. Manetti, Francesco Meazzini
{"title":"Deformations of Polystable Sheaves on Surfaces: Quadraticity Implies Formality","authors":"R. Bandiera, M. Manetti, Francesco Meazzini","doi":"10.17323/1609-4514-2022-22-2-239-263","DOIUrl":"https://doi.org/10.17323/1609-4514-2022-22-2-239-263","url":null,"abstract":"We study relations between the quadraticity of the Kuranishi family of a coherent sheaf on a complex projective scheme and the formality of the DG-Lie algebra of its derived endomorphisms. In particular, we prove that for a polystable coherent sheaf on a smooth complex projective surface the DG-Lie algebra of derived endomorphisms is formal if and only if the Kuranishi family is quadratic.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44897934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 7
Renormalization of Crossing Probabilities in the Planar Random-Cluster Model 平面随机聚类模型中交叉概率的重整化
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2019-01-24 DOI: 10.17323/1609-4514-2020-20-4-711-740
H. Duminil-Copin, V. Tassion
{"title":"Renormalization of Crossing Probabilities in the Planar Random-Cluster Model","authors":"H. Duminil-Copin, V. Tassion","doi":"10.17323/1609-4514-2020-20-4-711-740","DOIUrl":"https://doi.org/10.17323/1609-4514-2020-20-4-711-740","url":null,"abstract":"The study of crossing probabilities - i.e. probabilities of existence of paths crossing rectangles - has been at the heart of the theory of two-dimensional percolation since its beginning. They may be used to prove a number of results on the model, including speed of mixing, tails of decay of the connectivity probabilities, scaling relations, etc. In this article, we develop a renormalization scheme for crossing probabilities in the two-dimensional random-cluster model. The outcome of the process is a precise description of an alternative between four behaviors: \u0000- Subcritical: Crossing probabilities, even with favorable boundary conditions, converge exponentially fast to 0. \u0000- Supercritical: Crossing probabilities, even with unfavorable boundary conditions, converge exponentially fast to 1. \u0000- Critical discontinuous: Crossing probabilities converge to 0 exponentially fast with unfavorable boundary conditions and to 1 with favorable boundary conditions. \u0000- Critical continuous: Crossing probabilities remain bounded away from 0 and 1 uniformly in the boundary conditions. \u0000The approach does not rely on self-duality, enabling it to apply in a much larger generality, including the random-cluster model on arbitrary graphs with sufficient symmetry, but also other models like certain random height models.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44753109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 16
Smooth Quotients of Principally Polarized Abelian Varieties 主极化阿贝尔变种的光滑群
IF 0.8 4区 数学
Moscow Mathematical Journal Pub Date : 2019-01-21 DOI: 10.17323/1609-4514-2022-22-2-225-237
Robert Auffarth, G. Arteche
{"title":"Smooth Quotients of Principally Polarized Abelian Varieties","authors":"Robert Auffarth, G. Arteche","doi":"10.17323/1609-4514-2022-22-2-225-237","DOIUrl":"https://doi.org/10.17323/1609-4514-2022-22-2-225-237","url":null,"abstract":"We give an explicit characterization of all principally polarized abelian varieties $(A,Theta)$ such that there is a finite subgroup of automorphisms $G$ of $A$ that preserve the numerical class of $Theta$, and such that the quotient variety $A/G$ is smooth. We also give a complete classification of smooth quotients of Jacobian varieties of curves.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42109438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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