Enumerative invariants of stongly semipositive real symplectic manifolds
Résumé
Following the approach of Gromov and Witten, we define invariants under deformation of stongly semipositive real symplectic manifolds provided essentially that their real locus is $Pin^\pm$. These invariants provide lower bounds in real enumerative geometry, namely for the number of real rational J-holomorphic curves which realize a given homology class and pass through a given real configuration of points. In a first part of this paper, we obtain the correponding results for real projective convex manifolds using algebraic techniques.