Classification of Okamoto-Painlevé Pairs

2000/06/05 by Masa-Hiko Saito, Taro Takebe
Mathematics · #math.AG #msc:14D15 #msc:14J26

paper · pdf

published as Kobe Journal Math., Vol. 19, No.1-2. 2002 21--55 · 24 pages

arxiv created 2000/06/05 · arxiv updated 2009/11/30

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 \citeOka. We will give the complete classification of Okamoto-Painlevé pairs.

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