Projective structures, neighborhoods of rational curves and Painlev'e equations
Classical Analysis and ODEs
2021-06-18 v4 Complex Variables
Differential Geometry
Abstract
We investigate the duality between local (complex analytic) projective structures on surfaces and two dimensional (complex analytic) neighborhoods of rational curves having self-intersection +1. We study the analytic classification, existence of normal forms, pencil/fibration decomposition, infinitesimal symmetries. We deduce some transcendental result about Painlev'e equations.
Keywords
Cite
@article{arxiv.1707.07868,
title = {Projective structures, neighborhoods of rational curves and Painlev'e equations},
author = {Maycol Falla Luza and Frank Loray},
journal= {arXiv preprint arXiv:1707.07868},
year = {2021}
}
Comments
This version is a shortening of previous version v3. Some new results have been added, like prolongation of foliated structure in section 3.4, and non existence of foliated structure for many Painleve equations in section 6