Projective structures and neighborhoods of rational curves

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

1 IRMAR - Institut de Recherche Mathématique de Rennes

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.

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

Maycol Falla Luza, Frank Loray. Projective structures and neighborhoods of rational curves. 2018. ⟨hal-01567347v2⟩