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Journal Articles Moscow Mathematical Journal Year : 2022

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

Abstract

We 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.
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Dates and versions

hal-01567347 , version 1 (22-07-2017)
hal-01567347 , version 2 (11-06-2018)
hal-01567347 , version 3 (29-08-2018)
hal-01567347 , version 4 (16-06-2021)

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Cite

Maycol Falla Luza, Frank Loray. Projective structures, neighborhoods of rational curves and Painlev'e equations. Moscow Mathematical Journal, In press. ⟨hal-01567347v4⟩
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