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Classification of Okamoto-Painlevé Pairs

Masa-Hiko Saito·Taro Takebe
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Abstract

In this paper, we introduce the notion of an Okamoto-Painlevé pair (S, Y) which consists of a compact smooth complex surface S and an effective divisor Y on S satisfying certain conditions. Though spaces of initial values of Painlevé equations introduced by K. Okamoto give examples of Okamoto-Painleve pairs, we find a new example of Okamoto-Painlevé pairs not listed in \cite{Oka}. We will give the complete classification of Okamoto-Painlevé pairs.

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Masa-Hiko Saito, Taro Takebe. 2000-06-05. Classification of Okamoto-Painlevé Pairs. https://arxiv.org/abs/math/0006028

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