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Some Topological Applications of Theta Functions 函数的一些拓扑应用
Integrable Systems and Algebraic Geometry Pub Date : 2020-03-02 DOI: 10.1017/9781108773355.015
M. Spera
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引用次数: 0
Algebraic Geometry: A Celebration of Emma Previato’s 65th Birthday 代数几何:庆祝Emma Previato 65岁生日
Integrable Systems and Algebraic Geometry Pub Date : 2020-03-02 DOI: 10.1017/9781108773355.001
R. Donagi, T. Shaska
{"title":"Algebraic Geometry: A Celebration of Emma Previato’s 65th Birthday","authors":"R. Donagi, T. Shaska","doi":"10.1017/9781108773355.001","DOIUrl":"https://doi.org/10.1017/9781108773355.001","url":null,"abstract":"","PeriodicalId":110875,"journal":{"name":"Integrable Systems and Algebraic Geometry","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124432685","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: 1
Bergman Tau-Function: From Einstein Equations and Dubrovin-Frobenius Manifolds to Geometry of Moduli Spaces Bergman tau函数:从爱因斯坦方程和Dubrovin-Frobenius流形到模空间的几何
Integrable Systems and Algebraic Geometry Pub Date : 2020-03-02 DOI: 10.1017/9781108773355.008
D. Korotkin
{"title":"Bergman Tau-Function: From Einstein Equations and Dubrovin-Frobenius Manifolds to Geometry of Moduli Spaces","authors":"D. Korotkin","doi":"10.1017/9781108773355.008","DOIUrl":"https://doi.org/10.1017/9781108773355.008","url":null,"abstract":"","PeriodicalId":110875,"journal":{"name":"Integrable Systems and Algebraic Geometry","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133085012","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: 10
Frobenius Split Anticanonical Divisors Frobenius分裂反正则除数
Integrable Systems and Algebraic Geometry Pub Date : 2019-12-16 DOI: 10.1017/9781108773355.004
S'andor J. Kov'acs
{"title":"Frobenius Split Anticanonical Divisors","authors":"S'andor J. Kov'acs","doi":"10.1017/9781108773355.004","DOIUrl":"https://doi.org/10.1017/9781108773355.004","url":null,"abstract":"In this note I extend two theorems of Sommese regarding abelian varieties to arbitrary characteristic; that an abelian variety cannot be an ample divisor in a smooth projective variety and that a cone over an abelian variety of dimension at least two is not smoothable.","PeriodicalId":110875,"journal":{"name":"Integrable Systems and Algebraic Geometry","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122405612","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: 0
Noncommutative Cross-Ratio and Schwarz Derivative 非交换交叉比与施瓦茨导数
Integrable Systems and Algebraic Geometry Pub Date : 2019-05-03 DOI: 10.1017/9781108773355.017
V. Retakh, V. Rubtsov, G. Sharygin
{"title":"Noncommutative Cross-Ratio and Schwarz Derivative","authors":"V. Retakh, V. Rubtsov, G. Sharygin","doi":"10.1017/9781108773355.017","DOIUrl":"https://doi.org/10.1017/9781108773355.017","url":null,"abstract":"We present here a theory of noncommutative cross-ratio, Schwarz derivative and their connections and relations to the operator cross-ratio. We apply the theory to \"noncommutative elementary geometry\" and relate it to noncommutative integrable systems. We also provide a noncommutative version of the celebrated \"pentagramma mirificum\".","PeriodicalId":110875,"journal":{"name":"Integrable Systems and Algebraic Geometry","volume":"123 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122481782","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: 3
Solvable Dynamical Systems in the Plane with Polynomial Interactions 平面上具有多项式相互作用的可解动力系统
Integrable Systems and Algebraic Geometry Pub Date : 2019-04-02 DOI: 10.1017/9781108773287.006
F. Calogero, F. Payandeh
{"title":"Solvable Dynamical Systems in the Plane with Polynomial Interactions","authors":"F. Calogero, F. Payandeh","doi":"10.1017/9781108773287.006","DOIUrl":"https://doi.org/10.1017/9781108773287.006","url":null,"abstract":"In this paper we report a few examples of algebraically solvable dynamical systems characterized by 2 coupled Ordinary Differential Equations which read as follows: x_n = P(n) (x1, x2) , n = 1, 2 , with P(n) (x1, x2) specific polynomials of relatively low degree in the 2 dependent variables x1 = x1 (t) and x2 = x2 (t) . These findings are obtained via a new twist of a recent technique to identify dynamical systems solvable by algebraic operations, themselves explicitly identified as corresponding to the time evolutions of the zeros of polynomials the coefficients of which evolve according to algebraically solvable (systems of) evolution equations.","PeriodicalId":110875,"journal":{"name":"Integrable Systems and Algebraic Geometry","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133003141","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: 6
An Extension of Delsarte, Goethals and Mac Williams Theorem on Minimal Weight Codewords to a Class of Reed-Muller Type Codes 最小权码字的Delsarte、Goethals和Mac Williams定理在一类Reed-Muller型码上的推广
Integrable Systems and Algebraic Geometry Pub Date : 2019-03-22 DOI: 10.1017/9781108773355.010
C. Carvalho, V. Neumann
{"title":"An Extension of Delsarte, Goethals and Mac Williams Theorem on Minimal Weight Codewords to a Class of Reed-Muller Type Codes","authors":"C. Carvalho, V. Neumann","doi":"10.1017/9781108773355.010","DOIUrl":"https://doi.org/10.1017/9781108773355.010","url":null,"abstract":"In 1970 Delsarte, Goethals and Mac Williams published a seminal paper on generalized Reed-Muller codes where, among many important results, they proved that the minimal weight codewords of these codes are obtained through the evaluation of certain polynomials which are a specific product of linear factors, which they describe. In the present paper we extend this result to a class of Reed-Muller type codes defined on a product of (possibly distinct) finite fields of the same characteristic. The paper also brings an expository section on the study of the structure of low weight codewords, not only for affine Reed-Muller type codes, but also for the projective ones.","PeriodicalId":110875,"journal":{"name":"Integrable Systems and Algebraic Geometry","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127476991","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: 4
The Rigid Body Dynamics in an Ideal Fluid: Clebsch Top and Kummer Surfaces 理想流体中的刚体动力学:Clebsch顶面和Kummer面
Integrable Systems and Algebraic Geometry Pub Date : 2019-03-03 DOI: 10.1017/9781108773355.009
J. Françoise, Daisuke Tarama
{"title":"The Rigid Body Dynamics in an Ideal Fluid: Clebsch Top and Kummer Surfaces","authors":"J. Françoise, Daisuke Tarama","doi":"10.1017/9781108773355.009","DOIUrl":"https://doi.org/10.1017/9781108773355.009","url":null,"abstract":"This is an expository presentation of a completely integrable Hamiltonian system of Clebsch top under a special condition introduced by Weber. After a brief account on the geometric setting of the system, the structure of the Poisson commuting first integrals is discussed following the methods by Magri and Skrypnyk. Introducing supplementary coordinates, a geometric connection to Kummer surfaces, a typical class of K3 surfaces, is mentioned and also the system is linearized on the Jacobian of a hyperelliptic curve of genus two determined by the system. Further some special solutions contained in some vector subspace are discussed. Finally, an explicit computation of the action-angle coordinates is introduced.","PeriodicalId":110875,"journal":{"name":"Integrable Systems and Algebraic Geometry","volume":"151 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133591668","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: 1
Integrable Mappings from a Unified Perspective 统一视角下的可积映射
Integrable Systems and Algebraic Geometry Pub Date : 2019-01-23 DOI: 10.1017/9781108773287.011
Tova J. Brown, N. Ercolani
{"title":"Integrable Mappings from a Unified Perspective","authors":"Tova J. Brown, N. Ercolani","doi":"10.1017/9781108773287.011","DOIUrl":"https://doi.org/10.1017/9781108773287.011","url":null,"abstract":"Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random walks in random environments. The two models are integrable and our analysis uncovers the geometric sources of this integrability and uses this to conceptually explain the rigorous existence and structure of elegant closed form expressions for the associated probability distributions. Connections to asymptotic results are also described. The work here brings together ideas from a variety of fields including dynamical systems theory, probability theory, classical analogues of quantum spin systems, addtion laws on elliptic curves, and links between randomness and symmetry.","PeriodicalId":110875,"journal":{"name":"Integrable Systems and Algebraic Geometry","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126415323","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: 2
Positive One–Point Commuting Difference Operators∗† 正一点可交换差分算子*†
Integrable Systems and Algebraic Geometry Pub Date : 2018-10-25 DOI: 10.1017/9781108773287.017
G. S. Mauleshova, A. Mironov
{"title":"Positive One–Point Commuting Difference Operators∗†","authors":"G. S. Mauleshova, A. Mironov","doi":"10.1017/9781108773287.017","DOIUrl":"https://doi.org/10.1017/9781108773287.017","url":null,"abstract":"In this paper we study commuting difference operators containing a shift operator with only positive degrees. We construct examples of such operators in the case of hyperelliptic spectral curves.","PeriodicalId":110875,"journal":{"name":"Integrable Systems and Algebraic Geometry","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133674428","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: 1
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