2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66767We first present the construction of the moduli space of real pseudo-holomorphic curves in a given real symplectic manifold. Then, following the approach of Gromov and Witten, we construct invariants under deformation of real rational symplectic 4-manifolds. These invariants provide lower bounds for the number of real rational $J$-holomorphic curves in a given homology class passing through a given real configuration of points.31 pages, 8 figuresAlgebraic GeometrySymplectic Geometry14N10; 14P25 ; 53D05 ; 53D45Invariants of real symplectic 4-manifolds and lower bounds in real enumerative geometrytext