QUANTUM COHOMOLOGY OF THE HILBERT SCHEMEOF POINTS ON A_n-RESOLUTIONS

摘要

1.1. Overview. Given a quasiprojective surface S, the Hilbert scheme Hilbni(S)of m points on S parametrizes zero-dimensional subschemes of S of length m.The Hilbert scheme is a nonsingular irreducible quasiprojective algebraic varietyof dimension 2m. It contains an open dense set parametrizing configuration of mdistinct points and can be viewed as a crepant resolution of the symmetric productof S. The classical cohomology of these varieties has been well studied [N1, Gr, QW]and, as we shall explain later, admits a description in terms of the representationtheory of Heisenberg algebras.