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

Maycol Falla Luza (1) , Frank Loray (2)

1 UFF - Universidade Federal Fluminense [Rio de Janeiro]
2 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Projective structures; Painleve equations

Domaines: Analyse classique [math.CA]; Variables complexes [math.CV]; Géométrie différentielle [math.DG]

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