3:30 pm Thursday, September 1, 2016
Geometry Seminar: Ample Divisors on Hilbert Schemes of Points on Surfaces by Benjamin Schmidt (UT Austin) in RLM 9.166
The Hilbert scheme of n points on a smooth projective surface X is a smooth projective variety by a classical result of Fogarty. It is a nice compactification of the space of n unordered distinct points on X. A natural question about these spaces is to understand all possible embeddings into projective space. In algebraic geometry this can be encoded in the so called cone of ample divisors. Moreover, divisors on the boundary of this cone often times induce interesting birational morphisms. Using derived category techniques by Bayer and Macr , we solve this if X has Picard rank 1 and n is large. Moreover, we deal with the case where X is the blow up of the projective plane in 8 general points for any n, finishing work by Bertram and Coskun. Submitted by
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