Mathematical Physics
[Submitted on 11 Apr 2025
]
Title: Minimal algebraic solutions of the sixth equation of Painlevé
Title: Painlevé第六方程的最小代数解
Abstract: For each of the forty-eight exceptional algebraic solutions $u(x)$ of the sixth equation of Painlev\'e, we build the algebraic curve $P(u,x)=0$ of a degree conjectured to be minimal, then we give an optimal parametric representation of it. This degree is equal to the number of branches, except for fifteen solutions.
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