Hilbert schemes of points on the minimal resolution and soliton equations

Details Hilbert schemes of points on the minimal resolution and soliton equations Hilbert schemes of points on the minimal resolution and soliton equations

2004-04-29

arxiv.org/abs/math/0404540v2

Contemp. Math. 442 (2007), 435--462.

Mathematics

Quantum Algebra

minor changes, use of AMS Contemp. Math. format, latex, 28 pages, to appear in Lepowsky-Wilson volume

Scientific paper

The equivariant and ordinary cohomology rings of Hilbert schemes of points on the minimal resolution C^2//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 C^2//G are tau functions of 2-Toda hierarchies.

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