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arXiv · 1707.07868

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

Maycol Falla Luza·Frank Loray
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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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Maycol Falla Luza, Frank Loray. 2017-07-25. Projective structures, neighborhoods of rational curves and Painlev'e equations. https://arxiv.org/abs/1707.07868

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