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Hecke algebra action on twisted motivic Chern classes and K-theoretic stable envelopes 赫克代数对扭曲动机核类和 K 理论稳定包络的作用
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-18 DOI: 10.1007/s00208-024-02953-2
Jakub Koncki, Andrzej Weber
{"title":"Hecke algebra action on twisted motivic Chern classes and K-theoretic stable envelopes","authors":"Jakub Koncki, Andrzej Weber","doi":"10.1007/s00208-024-02953-2","DOIUrl":"https://doi.org/10.1007/s00208-024-02953-2","url":null,"abstract":"<p>Let <i>G</i> be a linear semisimple algebraic group and <i>B</i> its Borel subgroup. Let <span>({mathbb {T}}subset B)</span> be the maximal torus. We study the inductive construction of Bott–Samelson varieties to obtain recursive formulas for the twisted motivic Chern classes of Schubert cells in <i>G</i>/<i>B</i>. To this end we introduce two families of operators acting on the equivariant K-theory <span>({text {K}}_{mathbb {T}}(G/B)[y])</span>, the right and left Demazure–Lusztig operators depending on a parameter. The twisted motivic Chern classes coincide (up to normalization) with the K-theoretic stable envelopes. Our results imply wall-crossing formulas for a change of the weight chamber and slope parameters. The right and left operators generate a twisted double Hecke algebra. We show that in the type <i>A</i> this algebra acts on the Laurent polynomials. This action is a natural lift of the action on <span>({text {K}}_{mathbb {T}}(G/B)[y])</span> with respect to the Kirwan map. We show that the left and right twisted Demazure–Lusztig operators provide a recursion for twisted motivic Chern classes of matrix Schubert varieties.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"17 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185234","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
Local connectivity of boundaries of tame Fatou components of meromorphic functions 微函数驯服法图分量边界的局部连通性
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-17 DOI: 10.1007/s00208-024-02957-y
Krzysztof Barański, Núria Fagella, Xavier Jarque, Bogusława Karpińska
{"title":"Local connectivity of boundaries of tame Fatou components of meromorphic functions","authors":"Krzysztof Barański, Núria Fagella, Xavier Jarque, Bogusława Karpińska","doi":"10.1007/s00208-024-02957-y","DOIUrl":"https://doi.org/10.1007/s00208-024-02957-y","url":null,"abstract":"<p>We prove the local connectivity of the boundaries of invariant simply connected attracting basins for a class of transcendental meromorphic maps. The maps within this class need not be geometrically finite or in class <span>({mathcal {B}})</span>, and the boundaries of the basins (possibly unbounded) are allowed to contain an infinite number of post-singular values, as well as the essential singularity at infinity. A basic assumption is that the unbounded parts of the basins are contained in regions which we call ‘repelling petals at infinity’, where the map exhibits a kind of ‘parabolic’ behaviour. In particular, our results apply to a wide class of Newton’s methods for transcendental entire maps. As an application, we prove the local connectivity of the Julia set of Newton’s method for <span>(sin z)</span>, providing the first non-trivial example of a locally connected Julia set of a transcendental map outside class <span>({mathcal {B}})</span>, with an infinite number of unbounded Fatou components.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"24 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185236","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
Diffeomorphisms of 4-manifolds with boundary and exotic embeddings 有边界的 4-manifolds 的衍射和奇异嵌入
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-17 DOI: 10.1007/s00208-024-02974-x
Nobuo Iida, Hokuto Konno, Anubhav Mukherjee, Masaki Taniguchi
{"title":"Diffeomorphisms of 4-manifolds with boundary and exotic embeddings","authors":"Nobuo Iida, Hokuto Konno, Anubhav Mukherjee, Masaki Taniguchi","doi":"10.1007/s00208-024-02974-x","DOIUrl":"https://doi.org/10.1007/s00208-024-02974-x","url":null,"abstract":"<p>We define family versions of the invariant of 4-manifolds with contact boundary due to Kronheimer and Mrowka and use these to detect exotic diffeomorphisms of 4-manifolds with boundary. Further, we show the existence of the first example of exotic 3-spheres in a smooth closed 4-manifold with diffeomorphic complements.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"2 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185235","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
Finiteness of the stress in presence of closely located inclusions with imperfect bonding 在夹杂物位置紧密、结合不完全的情况下应力的精细度
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-14 DOI: 10.1007/s00208-024-02968-9
Shota Fukushima, Yong-Gwan Ji, Hyeonbae Kang, Xiaofei Li
{"title":"Finiteness of the stress in presence of closely located inclusions with imperfect bonding","authors":"Shota Fukushima, Yong-Gwan Ji, Hyeonbae Kang, Xiaofei Li","doi":"10.1007/s00208-024-02968-9","DOIUrl":"https://doi.org/10.1007/s00208-024-02968-9","url":null,"abstract":"<p>If two conducting or insulating inclusions are closely located, the gradient of the solution may become arbitrarily large as the distance between inclusions tends to zero, resulting in high concentration of stress in between two inclusions. This happens if the bonding of the inclusions and the matrix is perfect, meaning that the potential and flux are continuous across the interface. In this paper, we consider the case when the bonding is imperfect. We consider the case when there are two circular inclusions of the same radii with the imperfect bonding interfaces and prove that the gradient of the solution is bounded regardless of the distance between inclusions if the bonding parameter is finite. This result is of particular importance since the imperfect bonding interface condition is an approximation of the membrane structure of biological inclusions such as biological cells.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"1896 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185237","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
Bigness of tangent bundles and dynamical rigidity of Fano manifolds of Picard number 1 (with an appendix by Jie Liu) 皮卡尔数 1 的法诺流形的切线束大和动力学刚度（附刘杰的附录）
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-12 DOI: 10.1007/s00208-024-02955-0
Feng Shao, Guolei Zhong
{"title":"Bigness of tangent bundles and dynamical rigidity of Fano manifolds of Picard number 1 (with an appendix by Jie Liu)","authors":"Feng Shao, Guolei Zhong","doi":"10.1007/s00208-024-02955-0","DOIUrl":"https://doi.org/10.1007/s00208-024-02955-0","url":null,"abstract":"<p>Let <span>(f:Xrightarrow Y)</span> be a surjective morphism of Fano manifolds of Picard number 1 whose VMRTs at a general point are not dual defective. Suppose that the tangent bundle <span>(T_X)</span> is big. We show that <span>(f)</span> is an isomorphism unless <span>(Y)</span> is a projective space. As applications, we explore the bigness of the tangent bundles of complete intersections, del Pezzo manifolds, and Mukai manifolds, as well as their dynamical rigidity.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"7 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185238","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
Ax–Schanuel for variations of mixed Hodge structures 混合霍奇结构变化的 Ax-Schanuel
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-10 DOI: 10.1007/s00208-024-02958-x
Kenneth Chung Tak Chiu
{"title":"Ax–Schanuel for variations of mixed Hodge structures","authors":"Kenneth Chung Tak Chiu","doi":"10.1007/s00208-024-02958-x","DOIUrl":"https://doi.org/10.1007/s00208-024-02958-x","url":null,"abstract":"<p>We give properties of the real-split retraction of the mixed weak Mumford–Tate domain and prove the Ax–Schanuel property of period mappings arising from variations of mixed Hodge structures. An ingredient in the proof is the definability of the mixed period mapping obtained by Bakker–Brunebarbe–Klingler–Tsimerman. In comparison with preceding results, in the point counting step, we count rational points on definable quotients instead.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"80 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940005","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
Specialization maps for Scholze’s category of diamonds 舒尔茨钻石类别的特化图
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-08 DOI: 10.1007/s00208-024-02952-3
Ian Gleason
{"title":"Specialization maps for Scholze’s category of diamonds","authors":"Ian Gleason","doi":"10.1007/s00208-024-02952-3","DOIUrl":"https://doi.org/10.1007/s00208-024-02952-3","url":null,"abstract":"<p>We introduce the specialization map in Scholze’s theory of diamonds. We consider v-sheaves that “behave like formal schemes\" and call them kimberlites. We attach to them: a reduced special fiber, an analytic locus, a specialization map, a Zariski site, and an étale site. When the kimberlite comes from a formal scheme, our sites recover the classical ones. We prove that unramified <i>p</i>-adic Beilinson–Drinfeld Grassmannians are kimberlites with finiteness and normality properties.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"41 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940128","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
Monogamy of entanglement between cones 锥体间纠缠的一夫一妻制
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-07 DOI: 10.1007/s00208-024-02935-4
Guillaume Aubrun, Alexander Müller-Hermes, Martin Plávala
{"title":"Monogamy of entanglement between cones","authors":"Guillaume Aubrun, Alexander Müller-Hermes, Martin Plávala","doi":"10.1007/s00208-024-02935-4","DOIUrl":"https://doi.org/10.1007/s00208-024-02935-4","url":null,"abstract":"<p>A separable quantum state shared between parties <i>A</i> and <i>B</i> can be symmetrically extended to a quantum state shared between party <i>A</i> and parties <span>(B_1,ldots ,B_k)</span> for every <span>(kin textbf{N})</span>. Quantum states that are not separable, i.e., entangled, do not have this property. This phenomenon is known as “monogamy of entanglement”. We show that monogamy is not only a feature of quantum theory, but that it characterizes the minimal tensor product of general pairs of convex cones <span>(textsf{C}_A)</span> and <span>(textsf{C}_B)</span>: The elements of the minimal tensor product <span>(textsf{C}_Aotimes _{min } textsf{C}_B)</span> are precisely the tensors that can be symmetrically extended to elements in the maximal tensor product <span>(textsf{C}_Aotimes _{max } textsf{C}^{otimes _{max } k}_B)</span> for every <span>(kin textbf{N})</span>. Equivalently, the minimal tensor product of two cones is the intersection of the nested sets of <i>k</i>-extendible tensors. It is a natural question when the minimal tensor product <span>(textsf{C}_Aotimes _{min } textsf{C}_B)</span> coincides with the set of <i>k</i>-extendible tensors for some finite <i>k</i>. We show that this is universally the case for every cone <span>(textsf{C}_A)</span> if and only if <span>(textsf{C}_B)</span> is a polyhedral cone with a base given by a product of simplices. Our proof makes use of a new characterization of products of simplices up to affine equivalence that we believe is of independent interest.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"311 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940007","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
Calibrated representations of the double Dyck path algebra 双戴克路径代数的校准表示法
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-06 DOI: 10.1007/s00208-024-02937-2
Nicolle González, Eugene Gorsky, José Simental
{"title":"Calibrated representations of the double Dyck path algebra","authors":"Nicolle González, Eugene Gorsky, José Simental","doi":"10.1007/s00208-024-02937-2","DOIUrl":"https://doi.org/10.1007/s00208-024-02937-2","url":null,"abstract":"<p>The double Dyck path algebra <span>(mathbb {A}_{q,t})</span> and its polynomial representation first arose as a key figure in the proof of the celebrated Shuffle Theorem of Carlsson and Mellit. A geometric formulation for an equivalent algebra <span>(mathbb {B}_{q,t})</span> was then given by the second author and Carlsson and Mellit using the K-theory of parabolic flag Hilbert schemes. In this article, we initiate the systematic study of the representation theory of the double Dyck path algebra <span>(mathbb {B}_{q,t})</span>. We define a natural extension of this algebra and study its calibrated representations. We show that the polynomial representation is calibrated, and place it into a large family of calibrated representations constructed from posets satisfying certain conditions. We also define tensor products and duals of these representations, thus proving (under suitable conditions) the category of calibrated representations is generically monoidal. As an application, we prove that tensor powers of the polynomial representation can be constructed from the equivariant K-theory of parabolic Gieseker moduli spaces.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"43 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940008","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 isoperimetric problem in the Riemannian manifold admitting a non-trivial conformal vector field 容纳非三维共形向量场的黎曼流形中的等周问题
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-03 DOI: 10.1007/s00208-024-02954-1
Jiayu Li, Shujing Pan
{"title":"The isoperimetric problem in the Riemannian manifold admitting a non-trivial conformal vector field","authors":"Jiayu Li, Shujing Pan","doi":"10.1007/s00208-024-02954-1","DOIUrl":"https://doi.org/10.1007/s00208-024-02954-1","url":null,"abstract":"<p>In this article, we will study the isoperimetric problem by introducing a mean curvature type flow in the Riemannian manifold endowed with a non-trivial conformal vector field. This flow preserves the volume of the bounded domain enclosed by a star-shaped hypersurface and decreases the area of hypersurface under certain conditions. We will prove the long time existence and convergence of the flow. As a result, the isoperimetric inequality for such a domain is established. Especially, we solve the isoperimetric problem for the star-shaped hypersurfaces in the Riemannian manifold endowed with a closed, non-trivial conformal vector field, a wide class of warped product spaces studied by Guan, Li and Wang is included.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"75 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880496","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
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