Semisimple Frobenius structures at higher genus
代数几何
2007-05-23 v4
摘要
We describe genus g>1 potentials of semisimple Frobenius structures. Our formula can be considered as a definition in the axiomatic context of Frobenius manifolds. In Gromov-Witten theory, it becomes a conjecture expressing higher genus GW-invariants in terms of genus 0 GW-invariants of symplectic manifolds with generically semisimple quantum cup-product. The conjecture is supported by the corresponding theorem about equivariant GW-invariants of tori actions with isolated fixed points. The parallel theory of gravitational descendents is also presented.
引用
@article{arxiv.math/0008067,
title = {Semisimple Frobenius structures at higher genus},
author = {Alexander Givental},
journal= {arXiv preprint arXiv:math/0008067},
year = {2007}
}
备注
Exposition is improved according to reader's suggestions. To appear in IMRN