PIRSA:10050039 Conference

DOI10.48660/10050039

Conference/School: Connections in Geometry and Physics 2010

Liu, C. (2010). The coherent-constructible correspondence and homological mirror symmetry for toric varieties. Perimeter Institute. https://pirsa.org/10050039

Liu, Chiu-Chu. The coherent-constructible correspondence and homological mirror symmetry for toric varieties. Perimeter Institute, May. 08, 2010, https://pirsa.org/10050039 

@misc{ pirsa_PIRSA:10050039,
  doi = {10.48660/10050039},
  url = {https://pirsa.org/10050039},
  author = {Liu, Chiu-Chu},
  keywords = {},
  language = {en},
  title = {The coherent-constructible correspondence and homological mirror symmetry for toric varieties},
  publisher = {Perimeter Institute},
  year = {2010},
  month = {may},
  note = {PIRSA:10050039 see, \url{https://pirsa.org}}
}

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.

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