Classification of Okamoto-Painlevé Pairs

Details Classification of Okamoto-Painlevé Pairs Classification of Okamoto-Painlevé Pairs

2000-06-05

arxiv.org/abs/math/0006028v1

Kobe Journal Math., Vol. 19, No.1-2. 2002 21--55

Mathematics

Algebraic Geometry

24 pages

Scientific paper

In this paper, we introduce the notion of an Okamoto-Painlev\'e 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 Painlev\'e equations introduced by K. Okamoto give examples of Okamoto-Painleve pairs, we find a new example of Okamoto-Painlev\'e pairs not listed in \cite{Oka}. We will give the complete classification of Okamoto-Painlev\'e pairs.

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