Relative Gromov-Witten Invariants

Details Relative Gromov-Witten Invariants Relative Gromov-Witten Invariants

1999-07-23

arxiv.org/abs/math/9907155v3

Ann. of Math. (2), Vol. 157 (2003), no. 1, 45--96

Mathematics

Symplectic Geometry

AMS-LaTeX, 52 pages published version

Scientific paper

We define relative Gromov-Witten invariants of a symplectic manifold relative to a codimension two symplectic submanifold. These invariants are the key ingredients in the symplectic sum formula of [IP4]. The main step is the construction of a compact space of `V-stable' maps. Simple special cases include the Hurwitz numbers for algebraic curves and the enumerative invariants of Caporaso and Harris.

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