Grothendieck's dessins d'enfants, their deformations, and algebraic solutions of the sixth Painlevé and Gauss hypergeometric equations

A. V. Kitaev

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Grothendieck's dessins d'enfants, their deformations, and algebraic solutions of the sixth Painlevé and Gauss hypergeometric equations

机译：Grothendieck的dessins d'enfants，它们的变形以及第六Painlevé和Gauss超几何方程的代数解

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Grothendieck's dessins d'enfants are applied to the theory of the sixth Painlevé and Gauss hypergeometric functions, two classical special functions of iso- monodromy type. It is shown that higher-order transformations and the Schwarz table for the Gauss hypergeometric function are closely related to some particular Belyi functions. Moreover, deformations of the dessins d'enfants are introduced, and it is shown that one-dimensional deformations are a useful tool for construction of algebraic sixth Painlevé functions.

机译：格罗腾迪克的“ dessins d'enfants”被应用到第六个Painlevé和Gauss超几何函数的理论上，这是同等单调类型的两个经典特殊函数。结果表明，高斯超几何函数的高阶变换和Schwarz表与某些特定的Belyi函数密切相关。此外，引入了dessins d'enfant的变形，结果表明，一维变形是构造代数第六Painlevé函数的有用工具。

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《St. Petersburg mathematical journal》 |2006年第1期|共38页
作者
A. V. Kitaev;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Algebraic function; dessin d'enfant; hypergeometric function; isomonodromy deformation; Schlesinger deformations; the sixth Painleve equation;

机译：代数函数;desantin d'enfant;超几何函数;等等变形;Schlesinger变形;第六Painleve方程;

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1. Grothendieck's dessins d'enfants, their deformations, and algebraic solutions of the sixth Painlevé and Gauss hypergeometric equations [J] . A. V. Kitaev St. Petersburg mathematical journal . 2006,第1期

机译：Grothendieck的dessins d'enfants，它们的变形以及第六Painlevé和Gauss超几何方程的代数解
2. Algebraic solutions of the sixth Painlevé equation [J] . Oleg Lisovyy, Yuriy Tykhyy Journal of geometry and physics . 2014,第Null期

机译：第六Painlevé方程的代数解
3. Transformations RS42(3) of the Ranks ≤ 4 and Algebraic Solutions of the Sixth Painlevé Equation [J] . F. V. Andreev, A. V. Kitaev Communications in Mathematical Physics . 2002,第1期

机译：秩≤4的变换RS42（3）和第六个Painlevé方程的代数解
4. Invited Talk 3: Grobner Deformations of Hypergeometric Differential Equations [C] . Bernd Sturmfels International Symposium on Symbolic and Algebraic Computation . 1999

机译：邀请的谈话3：超高度差分方程的Grobner变形
5. Superintegrable Systems, Exceptional Polynomials and Solutions to Painlevé Equations [D] . Ritter, Lisa. 2021

机译：SuperIngeGleable Systems，特殊的多项式和Painlevé方程的解决方案
6. Geometric description of a discrete power function associated with the sixth Painlevé equation [O] . Nalini Joshi, Kenji Kajiwara, Tetsu Masuda, -1

机译：与第六个Painlevé方程相关的离散幂函数的几何描述
7. Dessins d'Enfants, Their Deformations and Algebraic the Sixth Painlev\'e and Gauss Hypergeometric Functions [O] . Kitaev, A. V. 2003

机译：Dessins d'Enfants，他们的变形和代数是第六个painlev \'e 和高斯超几何函数

Grothendieck's dessins d'enfants, their deformations, and algebraic solutions of the sixth Painlevé and Gauss hypergeometric equations

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