English

A Product Formula for Gromov-Witten Invariants

Symplectic Geometry 2010-03-16 v2 Differential Geometry

Abstract

We establish a product formula for Gromov-Witten invariants for closed, connected, relatively semi-positive Hamiltonian fibrations over any symplectic base. Furthermore, we show that the fibration projection induces a locally trivial (orbi-)fibration map from the moduli space of pseudo-holomorphic maps with marked points in the total space of the Hamiltonian fibration to the corresponding moduli space of pseudo-holomorphic maps with marked points in the base. We use this induced map to recover the product formula by means of integration. Finally, we give applications to c-splitting and symplectic uniruledness.

Keywords

Cite

@article{arxiv.0904.1492,
  title  = {A Product Formula for Gromov-Witten Invariants},
  author = {Clément Hyvrier},
  journal= {arXiv preprint arXiv:0904.1492},
  year   = {2010}
}

Comments

59 pages, no figure, changes in the presention, minor corrections, added proofs in the gluing section.

R2 v1 2026-06-21T12:49:46.346Z