中央研究院數學研究所

Algebraic Geometry Seminar

On the Hilb/Sym Correspondence

2026/01/02 (Fri.) 16:00~18:00

Date : 2026/01/02 (Fri.) 16:00~18:00
Location : Seminar Room 617, Institute of Mathematics (NTU Campus)
Speaker : Hsian-Hua Tseng (Ohio State University)
Organizer : Ionut Ciocan-Fontanine and Adeel Khan and Y.P. Lee (AS)
Abstract : For a smooth surface S, the Hilbert scheme of n points on S, Hilb(S,n), is smooth of dimension 2n. The Hilbert-Chow morphism Hilb(S,n)\to S^n/S_n is a crepant resolution of the (singular) n-fold symmetric product variety S^n/S_n associated to S. The so-called crepant resolution conjecture in Gromov-Witten theory predicts in this case explicit equalities between generating functions of Gromov-Witten invariants of Hilb(S,n) and generating functions of Gromov-Witten invariants of the symmetric product stack Sym(S,n). In this talk, we discuss the formulation of this conjecture and proofs in known cases.