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The theory of Nested Hilbert schemes on surfaces

Speaker: 
Artan Sheshmani
Institution: 
Harvard University
Schedule: 
Thursday, January 19, 2017 - 14:30
Location: 
A-136
Abstract: 

We construct natural virtual fundamental classes for nested Hilbert schemes on a nonsingular projective surface S. This allows us to define new invariants of S that recover some of the known important cases such as  Poincare invariants of D\"{urr-Kabanov-Okonek and the stable pair invariants of Kool-Thomas. In the case of the nested Hilbert scheme of points, we can express these invariants in terms of integrals over the products of Hilbert scheme of points on S, and relate them to the vertex operator formulas found by Carlsson-Okounkov. The virtual fundamental classes of the nested Hilbert schemes play a crucial role in the local Donaldson-Thomas theory of threefolds that I will talk about, in talk 2 (scheduled on Friday 20 14:30 at ICTP).

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