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arxiv: math/9907155 · v3 · submitted 1999-07-23 · 🧮 math.SG · math.AG· math.DG

Relative Gromov-Witten Invariants

classification 🧮 math.SG math.AGmath.DG
keywords invariantsrelativesymplecticgromov-wittenalgebraiccaporasocasescodimension
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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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