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• W2229611407 abstract "Higher dimensional analogs of the Painlev'e equations have been proposed from various aspects. In recent studies, 4-dimensional analogs of the Painlev'e equations were classified into 40 types. The aim of the present paper is to geometrically characterize these 40 types of equations. For this purpose, we study the autonomous limit of these equations and degeneration of their spectral curves. We obtain two functionally independent conserved quantities $H_1$ and $H_2$ for each system. We construct fibrations whose fiber at a general point $h_i $ is the spectral curve of the system with $H_i=h_i$ for $i=1, 2$. The singular fibers at $H_{i}=infty$ are one of the degenerate curves of genus 2 classified by Namikawa and Ueno. Liu's algorithm enables us to give degeneration type of spectral curves for our 40 types of integrable systems. This result is analogous to the following observation; spectral curve fibrations of the autonomous 2-dimensional Painlev'e equations $P_{rm I}$, $P_{rm II}$, $P_{rm IV}$, $P_{rm III}^{D_8}$, $P_{rm III}^{D_7}$, $P_{rm III}^{D_6}$, $P_{V}$ and $P_{rm VI}$ are elliptic surfaces with the singular fiber at $H=infty$ of Dynkin type $E_8^{(1)}$, $E_7^{(1)}$, $E_6^{(1)}$, $D_8^{(1)}$, $D_7^{(1)}$, $D_6^{(1)}$, $D_5^{(1)}$ and $D_4^{(1)}$, respectively." @default.
• W2229611407 created "2016-06-24" @default.
• W2229611407 creator A5048254305 @default.
• W2229611407 date "2015-05-05" @default.
• W2229611407 modified "2023-09-27" @default.
• W2229611407 title "Autonomous limit of 4-dimensional Painlev'e-type equations and degeneration of curves of genus two" @default.
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• W2229611407 doi "https://doi.org/10.48550/arxiv.1505.00885" @default.
• W2229611407 hasPublicationYear "2015" @default.
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