English

Strengthening the Cohomological Crepant Resolution Conjecture for Hilbert-Chow morphisms

Algebraic Geometry 2013-07-15 v2

Abstract

Given any smooth toric surface S, we prove a SYM-HILB correspondence which relates the 3-point, degree zero, extended Gromov-Witten invariants of the n-fold symmetric product stack [Sym^n(S)] of S to the 3-point extremal Gromov-Witten invariants of the Hilbert scheme Hilb^n(S) of n points on S. As we do not specialize the values of the quantum parameters involved, this result proves a strengthening of Ruan's Cohomological Crepant Resolution Conjecture for the Hilbert-Chow morphism from Hilb^n(S) to Sym^n(S) and yields a method of reconstructing the cup product for Hilb^n(S) from the orbifold invariants of [Sym^n(S)].

Keywords

Cite

@article{arxiv.1112.6123,
  title  = {Strengthening the Cohomological Crepant Resolution Conjecture for Hilbert-Chow morphisms},
  author = {Wan Keng Cheong},
  journal= {arXiv preprint arXiv:1112.6123},
  year   = {2013}
}

Comments

Revised version