PIRSA:10050038
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Motivic degree zero Donaldson  Thomas invariants Speaker(s): Jim Bryan
Abstract: The Hilbert scheme X[n] of n points on variety X parameterizes length n, zero dimensional subschemes of X. When X is a smooth surface, X[n] is also smooth and a beautiful formula for its motive was determined by Gottsche. When X is a threefold, X[n] is in general singular, of the wrong dimension, and reducible. However if X is a smooth CalabiYau threefold, X[n] has a canonical virtual motive  a motification of the degree zero DonaldsonThomas invariants. We give a formula analogous to Gottsche's for the virtual motive of X[n]. The key computation gives a qrefinement of the classical formula of MacMahon which counts 3D partitions.
Date: 08/05/2010  1:45 pm
Collection: Connections in Geometry and Physics 2010
