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Invariants of real symplectic 4-manifolds and lower bounds in real enumerative geometry

Jean-Yves Welschinger
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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, 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.

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Jean-Yves Welschinger. 2003-03-12. Invariants of real symplectic 4-manifolds and lower bounds in real enumerative geometry. https://arxiv.org/abs/math/0303145

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