Abstract or Additional Information
Roughly speaking, a toric degeneration of a variety X is a (flat) family of irreducible varieties X_t such that the 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 show this by proving the stronger result that any graded algebra R has a full rank valuation with finitely generated value semigroup. This general result has far reaching 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. The main part of the work is due to Takuya Murata and will appear in his Ph.D. thesis. I will try to cover needed definitions and background in order to understand the main results of the talk. For the most part, the talk should be understandable for graduate students with basic background in algebra and geometry.