Strengthening the Cohomological Crepant Resolution Conjecture for Hilbert-Chow morphisms

الأصل · EN

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 [Symⁿ(S)] of S to the 3-point extremal Gromov-Witten invariants of the Hilbert scheme Hilbⁿ(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 Hilbⁿ(S) to Symⁿ(S) and yields a method of reconstructing the cup product for Hilbⁿ(S) from the orbifold invariants of [Symⁿ(S)].