Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2003, March 25.

Abstract:
We 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 \cite{Gro,Wit,RT}, 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.

Mathematics Subject Classification (2000): 14N10, 14P25 , 53D05 , 53D45.

Keywords and Phrases: Symplectic manifold, real algebraic curve, moduli space, enumerative geometry.

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