Classification of Okamoto-Painlev\'e Pairs
Algebraic Geometry
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0006028,
title = {Classification of Okamoto-Painlev\'e Pairs},
author = {Masa-Hiko Saito and Taro Takebe},
journal= {arXiv preprint arXiv:math/0006028},
year = {2007}
}
Comments
24 pages