Back to Algebraic Geometry Seminar: Fall 2018
Algebraic Geometry Seminar
Date: Tuesday, Sep 4, 2018
Time: 3:30PM - 4:30PM
Location: LCB 222
Harold Blum
University of Utah
Title |
Moduli of uniformly K-stable Fano varieties |
Abstract |
In order to have a well behaved moduli functor for Fano varieties, it seems natural to restrict oneself to Fano varieties that are K-polystable. Recall, K-stability is an algebraic notion that characterizes when a smooth Fano variety admits a Kahler-Einstein metric. In this talk, we consider the behavior of uniform K-stability (a strengthening of K-stability) in families. We will explain that uniform K-stability is an open condition in Q-Fano families and the moduli functor of uniformly K-stable Q-Fano varieties is separated. Together with a boundedness result of C. Jiang, these results yield a separated DM stack paratmerizing uniformly K-stable Fano varieties of fixed dimension and volume. This is joint work with Yuchen Liu and Chenyang Xu. |
Algebraic Geometry