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arXiv.org e-Print Archive
Preprint . 2017
Data sources: arXiv.org e-Print Archive
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Moscow Mathematical Journal
Article . 2023 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2017
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Projective Structures, Neighborhoods of Rational Curves and Painlevé equations

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Feb 2023Embargo end date: 01 Jan 2017Publisher:National Research University, Higher School of Economics (HSE)Journal:Moscow Mathematical Journal, volume 23, pages 59-95 (eissn: 1609-4514, Copyright policy )Funded by:UKRI | Light-weighting Children’..., ANR | Foliage
Authors: Falla Luza, Maycol; Loray, Frank;

doi: 10.17323/1609-4514-2023-23-1-59-95 , 10.48550/arxiv.1707.07868

arXiv: http://arxiv.org/abs/1707.07868

Projective Structures, Neighborhoods of Rational Curves and Painlevé equations

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.

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

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Keywords

Mathematics - Differential Geometry, Painleve equations, Mathematics - Complex Variables, [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA], 510, Projective structures, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Mathematics - Classical Analysis and ODEs, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], Classical Analysis and ODEs (math.CA), FOS: Mathematics, Complex Variables (math.CV), [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Top 10%
Average
Average
Green