PIRSA:10050038

Motivic degree zero Donaldson - Thomas invariants

Bryan, J. (2010). Motivic degree zero Donaldson - Thomas invariants. Perimeter Institute. https://pirsa.org/10050038

Bryan, Jim. Motivic degree zero Donaldson - Thomas invariants. Perimeter Institute, May. 08, 2010, https://pirsa.org/10050038 

          @misc{ pirsa_PIRSA:10050038,
            doi = {10.48660/10050038},
            url = {https://pirsa.org/10050038},
            author = {Bryan, Jim},
            keywords = {},
            language = {en},
            title = {Motivic degree zero Donaldson - Thomas invariants},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {may},
            note = {PIRSA:10050038 see, \url{https://pirsa.org}}
          }

Jim Bryan University of British Columbia

Talk numberPIRSA:10050038
DOI10.48660/10050038
Collection
Talk Type Conference

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.