Projective structures, neighborhoods of rational curves and Painlev'e equations

2017/07/25 by Maycol Falla Luza, Luza, Maycol Falla, Frank Loray +1
Mathematics · #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.CA #math.CV #math.DG

paper · pdf · doi:10.48550/arxiv.1707.07868

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

arxiv created 2021/06/17 · arxiv updated 2021/06/18

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.

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