Gromov-Witten Invariants of Symplectic Sums

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

The natural sum operation for symplectic manifolds is defined by gluing along codimension two submanifolds. Specifically, let X be a symplectic 2n-manifold with a symplectic (2n-2)-submanifold V. Given a similar pair (Y,W) with a symplectic identification V=W and a complex anti-linear isomorphism between the normal bundles of V and W, we can form the symplectic sum Z=X # Y. This note announces a general formula for computing the Gromov-Witten invariants of the sum Z in terms of relative Gromov-Witten invariants of (X,V) and (Y,W). Two applications are presented: a short derivation of the Caporaso-Harris formula [CH], and new proof that the rational enumerative invariants of the rational elliptic surface are given by the ``modular form'' (5.2).
AMS-LaTeX, 13 pages; repaginated and 7 typos fixed

Keywords

Symplectic Geometry, Algebraic Geometry

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/76993

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9806013
 http://arxiv.org/abs/math/9806013

Collections

arXiv