Relative Gromov-Witten invariants

Eleny-Nicoleta Ionel; Thomas H. Parker

doi:https://doi.org/10.4007/annals.2003.157.45

Pages 45-96 from Volume 157 (2003), Issue 1 by Eleny-Nicoleta Ionel, Thomas H. Parker

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.

Mathematical Subject Classification

Primary 2000: 14N35, 53D05

Milestones

Received: 25 July 1999
Revised: 25 October 2000
Accepted: 23 October 2001
Published online: January 2003

Authors

Eleny-Nicoleta Ionel

Current address:

Department of Mathematics, Stanford University, Stanford, CA 94305-2125

Thomas H. Parker

Department of Mathematics, Michigan State University, East Lansing, MI 48824