##### Department of Mathematics,

University of California San Diego

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### Math 208 - Algebraic Geometry

## Harold Blum

#### University of Utah

## Openness of K-stability for Fano varieties

##### Abstract:

Until recently, it was unclear if there was a natural way to construct (compactified) moduli spaces of Fano varieties. One approach to solving this problem is the K-moduli Conjecture, which predicts that K-polystable Fano varieties of fixed dimension and volume are parametrized by a projective good moduli space. In this talk, I will survey recent progress on this conjecture and discuss a result with Yuchen Liu and Chenyang Xu proving the openness of K-stability (a step in constructing K-moduli spaces).

Host: James McKernan

### November 22, 2019

### 12:45 PM

### AP&M 7321

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