Invariants de Welschinger

Abstract

This is an overview of some of the invariants that were discovered by Welschinger in the context of enumerative real algebraic geometry. Their definition finds a natural setup in real symplectic geometry. In particular, they can be studied using techniques from symplectic field theory, of which we also give a sample. Welschinger invariants are real analogues of certain Gromov-Witten invariants. This article is an extended set of notes for a talk at the Bourbaki seminar in April 2011.

Séminaire BOURBAKI, Avril 2011, 63ème année, 2010-2011, no.1036. To appear in Astérisque. 30 pages, 3 figures, French