Strengthening the Cohomological Crepant Resolution Conjecture for Hilbert-Chow morphisms

Details Strengthening the Cohomological Crepant Resolution Conjecture for Hilbert-Chow morphisms Strengthening the Cohomological Crepant Resolution Conjecture for Hilbert-Chow morphisms

2011-12-28

arxiv.org/abs/1112.6123v1

Mathematics

Algebraic Geometry

Scientific paper

Given any smooth toric surface S, we prove a SYM-HILB correspondence which relates the 3-point, degree 0, 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 in 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 of Hilb^n(S) from the orbifold invariants of [Sym^n(S)].

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