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Strengthening the Cohomological Crepant Resolution Conjecture for Hilbert-Chow morphisms (1112.6123v2)

Published 28 Dec 2011 in math.AG

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 [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)].

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