Strengthening the cohomological crepant resolution conjecture for Hilbert-Chow morphisms

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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 Hilbn(S) → Symn(S) and yields a method of reconstructing the cup product for Hilbn(S) from the orbifold invariants of [Symn(S)].

Original languageEnglish
Pages (from-to)45-72
Number of pages28
JournalMathematische Annalen
Volume356
Issue number1
DOIs
Publication statusPublished - 2013 Jan 1

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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