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

Loray, Frank

Luza, Maycol Falla

English

arXiv

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.International audienceWe investigate the duality between local (complex analytic) projec- tive 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

Projective structures and neighborhoods of rational curves

Abstract

Similar works

Full text

Available Versions

HAL-Rennes 1