Hilbert schemes of points on the minimal resolution and soliton equations
Abstract
The equivariant and ordinary cohomology rings of Hilbert schemes of points on the minimal resolution C2//G for cyclic G are studied using vertex operator technique, and connections between these rings and the class algebras of wreath products are explicitly established. We further show that certain generating functions of equivariant intersection numbers on the Hilbert schemes and related moduli spaces of sheaves on C2//G are tau functions of 2-Toda hierarchies.
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