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

@inproceedings{Luza2017ProjectiveSN, title={Projective structures, neighborhoods of rational curves and Painlev'e equations}, author={M. F. Luza and F. Loray}, year={2017} }

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 Painlevé equations. Part of the results were announced in [20]; an extended version is available in [21].

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