PIRSA:10050039  ( MP4 Medium Res , MP3 , PDF ) Which Format?
The coherent-constructible correspondence and homological mirror symmetry for toric varieties
Speaker(s): Chiu-Chu Liu
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 Calabi-Yau threefold, X[n] has a canonical virtual motive --- a motification of the degree zero Donaldson-Thomas invariants. We give a formula analogous to Gottsche's for the virtual motive of X[n]. The key computation gives a q-refinement of the classical formula of MacMahon which counts 3D partitions.
Date: 08/05/2010 - 3:15 pm
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