|Date: Wednesday, October 11, 2017
Location: 4096 East Hall (4:10 PM to 5:30 PM)
Title: Toric degenerations of projective varieties
Abstract: Roughly speaking, a toric degeneration of a variety X is a (flat) family (over affine line) of irreducible varieties X_t such that for nonzero t, X_t is isomorphic to X and X_0 is a (not necessarily normal) toric variety. I will present the new result that any projective variety has a toric degeneration. We prove this by showing that any graded algebra R has a full rank valuation with a finitely generated value semigroup. This general result has interesting consequences in a number of areas which I will briefly mention if there is time. This is a joint work with Chris Manon and Takuya Murata. For the most part, the talk should be understandable for graduate students with basic background in algebra and geometry.
Speaker: Kiumars Kaveh
Institution: University of Pittsburgh