Two point extremal Gromov-Witten invariants of Hilbert schemes of points on surfaces

2007/03/24 by Li, Jun, Li, Wei-Ping
#14C05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0703717

Abstract

Given an algebraic surface X, the Hilbert scheme X^[n] of n-points on X admits a contraction morphism to the n-fold symmetric product X⁽ⁿ⁾ with the extremal ray generated by a class β_n of a rational curve. We determine the two point extremal GW-invariants of X^[n] with respect to the class dβ_n for a simply-connected projective surface X and the quantum first Chern class operator of the tautological bundle on X^[n]. The methods used are vertex algebraic description of H^*(X^[n]), the localization technique applied to X=\mathbb P², and a generalization of the reduction theorem of Kiem-J. Li to the case of meromorphic 2-forms.

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