TY - JOUR
T1 - Strengthening the cohomological crepant resolution conjecture for Hilbert-Chow morphisms
AU - Cheong, Wan Keng
N1 - Funding Information:
Many thanks are due to Tom Graber, who introduced me to the fascinating world of algebraic geometry. This paper has benefited greatly from his inspiring ideas and helpful suggestions. I am also pleased to thank the referee for useful comments. A portion of this paper was written under support from the National Science Council, Taiwan.
PY - 2013/5
Y1 - 2013/5
N2 - 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)].
AB - 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)].
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U2 - 10.1007/s00208-012-0833-x
DO - 10.1007/s00208-012-0833-x
M3 - Article
AN - SCOPUS:84875739473
SN - 0025-5831
VL - 356
SP - 45
EP - 72
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 1
ER -