Surfaces elliptiques réelles et inégalité de Ragsdale-Viro
Résumé
On a real regular elliptic surface without multiple fiber, the Betti number h1 and the Hodge number h1,1 are related by h1<=h1,1. We prove that it's always possible to deform such algebraic surface to obtain h1=h1,1. Furthermore, we can impose that each homology class can be represented by a real algebraic curve. We use a real version of the modular construction of elliptic surfaces.