Relative Gromov-Witten Invariants
Abstract
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- July 1999
- DOI:
- arXiv:
- arXiv:math/9907155
- Bibcode:
- 1999math......7155I
- Keywords:
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- Symplectic Geometry;
- Algebraic Geometry;
- Differential Geometry
- E-Print:
- AMS-LaTeX, 52 pages published version