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Emergent Geometry of KP Hierarchy KP 层次结构的新兴几何学
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-01-15 DOI: 10.1007/s10114-024-1492-z
Jian Zhou
{"title":"Emergent Geometry of KP Hierarchy","authors":"Jian Zhou","doi":"10.1007/s10114-024-1492-z","DOIUrl":"https://doi.org/10.1007/s10114-024-1492-z","url":null,"abstract":"<p>We explain how to construct a quantum deformation of a spectral curve associated to a tau-function of the KP hierarchy. This construction is applied to Witten–Kontsevich tau-function to give a natural explanation of some earlier work. We also apply it to higher Weil–Petersson volumes and Witten’s r-spin intersection numbers.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Quantum Curve and Bilinear Fermionic Form for the Orbifold Gromov–Witten Theory of ℙ[r] ℙ[r]的轨道格罗莫夫-维滕理论的量子曲线和双线性费米子形式
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-01-15 DOI: 10.1007/s10114-024-1633-4
Chong Yao Chen, Shuai Guo
{"title":"Quantum Curve and Bilinear Fermionic Form for the Orbifold Gromov–Witten Theory of ℙ[r]","authors":"Chong Yao Chen, Shuai Guo","doi":"10.1007/s10114-024-1633-4","DOIUrl":"https://doi.org/10.1007/s10114-024-1633-4","url":null,"abstract":"<p>We construct the quantum curve for the Baker–Akhiezer function of the orbifold Gromov–Witten theory of the weighted projective line ℙ[<i>r</i>]. Furthermore, we deduce the explicit bilinear Fermionic formula for the (stationary) Gromov–Witten potential via the lifting operator contructed from the Baker–Akhiezer function.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On a Formation of Singularities of Solutions to Soliton Equations Represented by L, A, B-triples 论 L、A、B 三元组表示的孤子方程解奇异点的形成
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-01-05 DOI: 10.1007/s10114-024-2324-x
Iskander A. Taimanov
{"title":"On a Formation of Singularities of Solutions to Soliton Equations Represented by L, A, B-triples","authors":"Iskander A. Taimanov","doi":"10.1007/s10114-024-2324-x","DOIUrl":"https://doi.org/10.1007/s10114-024-2324-x","url":null,"abstract":"<p>We discuss the mechanism of formation of singularities of solutions to the Novikov–Veselov, modified Novikov–Veselov, and Davey–Stewartson II (DSII) equations obtained by the Moutard type transformations. These equations admit the <i>L, A, B</i>-triple presentation, the generalization of the <i>L, A</i>-pairs for 2+1-soliton equations. We relate the blow-up of solutions to the non-conservation of the zero level of discrete spectrum of the <i>L</i>-operator. We also present a class of exact solutions, of the DSII system, which depend on two functional parameters, and show that all possible singularities of solutions to DSII equation obtained by the Moutard transformation are indeterminancies, i.e., points when approaching which in different spatial directions the solution has different limits.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On Differential Equations of Integrable Billiard Tables 论积分台球桌的微分方程
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-01-05 DOI: 10.1007/s10114-024-2450-5
Vladimir Dragović, Andrey E. Mironov
{"title":"On Differential Equations of Integrable Billiard Tables","authors":"Vladimir Dragović, Andrey E. Mironov","doi":"10.1007/s10114-024-2450-5","DOIUrl":"https://doi.org/10.1007/s10114-024-2450-5","url":null,"abstract":"<p>We introduce a method to find differential equations for functions which define tables, such that associated billiard systems admit a local first integral. We illustrate this method in three situations: the case of (locally) integrable wire billiards, for finding surfaces in ℝ<sup>3</sup> with a first integral of degree one in velocities, and for finding a piece-wise smooth surface in ℝ<sup>3</sup> homeomorphic to a torus, being a table of a billiard admitting two additional first integrals.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Gluing Affine Vortices 粘合仿射漩涡
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-01-05 DOI: 10.1007/s10114-024-2248-5
Guang Bo Xu
{"title":"Gluing Affine Vortices","authors":"Guang Bo Xu","doi":"10.1007/s10114-024-2248-5","DOIUrl":"https://doi.org/10.1007/s10114-024-2248-5","url":null,"abstract":"<p>We provide an analytical construction of the gluing map for stable affine vortices over the upper half plane with the Lagrangian boundary condition. This result is a necessary ingredient in studies of the relation between gauged sigma model and nonlinear sigma model, such as the closed or open quantum Kirwan map.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A Tropical View on Landau–Ginzburg Models 兰道-金兹堡模型的热带视角
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-01-05 DOI: 10.1007/s10114-024-2295-y
Michael Carl, Max Pumperla, Bernd Siebert
{"title":"A Tropical View on Landau–Ginzburg Models","authors":"Michael Carl, Max Pumperla, Bernd Siebert","doi":"10.1007/s10114-024-2295-y","DOIUrl":"https://doi.org/10.1007/s10114-024-2295-y","url":null,"abstract":"<p>This paper, largely written in 2009/2010, fits Landau–Ginzburg models into the mirror symmetry program pursued by the last author jointly with Mark Gross since 2001. This point of view transparently brings in tropical disks of Maslov index 2 via the notion of broken lines, previously introduced in two dimensions by Mark Gross in his study of mirror symmetry for ℙ<sup>2</sup>. A major insight is the equivalence of properness of the Landau–Ginzburg potential with smoothness of the anticanonical divisor on the mirror side. We obtain proper superpotentials which agree on an open part with those classically known for toric varieties. Examples include mirror LG models for non-singular and singular del Pezzo surfaces, Hirzebruch surfaces and some Fano threefolds.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
GUE via Frobenius Manifolds. I. From Matrix Gravity to Topological Gravity and Back 通过弗罗贝尼乌斯流形的 GUE。I. 从矩阵引力到拓扑引力再到拓扑引力
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-01-05 DOI: 10.1007/s10114-024-2258-3
Di Yang
{"title":"GUE via Frobenius Manifolds. I. From Matrix Gravity to Topological Gravity and Back","authors":"Di Yang","doi":"10.1007/s10114-024-2258-3","DOIUrl":"https://doi.org/10.1007/s10114-024-2258-3","url":null,"abstract":"<p>Dubrovin establishes a certain relationship between the GUE partition function and the partition function of Gromov–Witten invariants of the complex projective line. In this paper, we give a direct proof of Dubrovin’s result. We also present in a diagram the recent progress on topological gravity and matrix gravity.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Normal Crossings Singularities for Symplectic Topology: Structures 交点拓扑学的法线交叉奇异性：结构
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-01-05 DOI: 10.1007/s10114-024-2042-4
Mohammad Farajzadeh-Tehrani, Mark Mclean, Aleksey Zinger
{"title":"Normal Crossings Singularities for Symplectic Topology: Structures","authors":"Mohammad Farajzadeh-Tehrani, Mark Mclean, Aleksey Zinger","doi":"10.1007/s10114-024-2042-4","DOIUrl":"https://doi.org/10.1007/s10114-024-2042-4","url":null,"abstract":"<p>Our previous papers introduce topological notions of normal crossings symplectic divisor and variety, show that they are equivalent, in a suitable sense, to the corresponding geometric notions, and establish a topological smoothability criterion for normal crossings symplectic varieties. The present paper constructs a blowup, a complex line bundle, and a logarithmic tangent bundle naturally associated with a normal crossings symplectic divisor and determines the Chern class of the last bundle. These structures have applications in constructions and analysis of various moduli spaces. As a corollary of the Chern class formula for the logarithmic tangent bundle, we refine Aluffi’s formula for the Chern class of the tangent bundle of the blowup at a complete intersection to account for the torsion and extend it to the blowup at the deepest stratum of an arbitrary normal crossings divisor.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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-shadowing for ℤd-actions ℤd-作用的准阴影
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-12-29 DOI: 10.1007/s10114-023-1681-1
Juan Pan, Xian Kun Ren, Yun Hua Zhou
{"title":"Quasi-shadowing for ℤd-actions","authors":"Juan Pan, Xian Kun Ren, Yun Hua Zhou","doi":"10.1007/s10114-023-1681-1","DOIUrl":"https://doi.org/10.1007/s10114-023-1681-1","url":null,"abstract":"<p>A diffeomorphism is non-uniformly partially hyperbolic if it preserves an ergodic measure with at least one zero Lyapunov exponent. We prove that a <i>C</i><sup>1</sup>-smooth ℤ<sup><i>d</i></sup>-action has the quasi-shadowing property if one of the generators is <i>C</i><sup>1+<i>α</i></sup> (<i>α</i> &gt; 0) non-uniformly partially hyperbolic.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139067344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Continuous Orbit Equivalence of Semigroup Actions 半群作用的连续轨道等价性
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-12-29 DOI: 10.1007/s10114-023-2608-6
Xiang Qi Qiang, Cheng Jun Hou
{"title":"Continuous Orbit Equivalence of Semigroup Actions","authors":"Xiang Qi Qiang, Cheng Jun Hou","doi":"10.1007/s10114-023-2608-6","DOIUrl":"https://doi.org/10.1007/s10114-023-2608-6","url":null,"abstract":"<p>We introduce notions of continuous orbit equivalence and its one-sided version for countable left Ore semigroup actions on compact spaces by surjective local homeomorphisms, and characterize them in terms of the corresponding transformation groupoids and their operator algebras. In particular, we show that two essentially free semigroup actions on totally disconnected compact spaces are continuously orbit equivalent if and only if there is a canonical abelian subalgebra preserving <i>C</i>*-isomorphism between the associated transformation groupoid <i>C</i>*-algebras. We also give some examples of orbit equivalence, consider the special case of semigroup actions by homeomorphisms and relate continuous orbit equivalence of semigroup actions to that of the associated group actions.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139067346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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