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Moscow Mathematical Journal, 2023, Volume 23, Number 1, Pages 59–95
DOI: https://doi.org/10.17323/1609-4514-2023-23-1-59-95 (Mi mmj846) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Projective structures, neighborhoods of rational curves and Painlevé equations

Maycol Falla Luzaa, Frank Lorayb

a UFF, Universidad Federal Fluminense, rua Mário Santos Braga S/N, Niterói, RJ, Brasil
b Univ Rennes 1, CNRS, IRMAR, UMR 6625, F-35000 Rennes, France
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DOI: https://doi.org/10.17323/1609-4514-2023-23-1-59-95
URL: https://www.mathjournals.org/mmj/2023-023-001/2023-023-001-004.html
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 Painlevé equations. Part of the results were announced in Comptes rendus in 2016; an extended version is available at https://arxiv.org/pdf/1707.07868v3.pdf.
Key words and phrases: foliation, projective structure, rational curves.
Document Type: Article
MSC: 53B05, 32G13, 34M55
Language: English
Citation: Maycol Falla Luza, Frank Loray, “Projective structures, neighborhoods of rational curves and Painlevé equations”, Mosc. Math. J., 23:1 (2023), 59–95
Citation in format AMSBIB
\Bibitem{LuzLor23}
\by Maycol~Falla~Luza, Frank~Loray
\paper Projective structures, neighborhoods of rational curves and Painlev\'e equations
\jour Mosc. Math.~J.
\yr 2023
\vol 23
\issue 1
\pages 59--95
\mathnet{http://mi.mathnet.ru/mmj846}
\crossref{https://doi.org/10.17323/1609-4514-2023-23-1-59-95}
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    • This publication is cited in the following 4 articles:
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