##### Department of Mathematics,

University of California San Diego

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### Math 208 - Algebraic Geometry Seminar

## Valery Alexeev

#### University of Georgia

## Compact moduli spaces of K3 surfaces

##### Abstract:

I will explain recent results on modular, geometrically meaningful compactifications of moduli spaces of K3 surfaces, most of which are joint with Philip Engel. A key notion is that of a recognizable divisor: a canonical choice of a divisor in a multiple of the polarization that can be canonically extended to any Kulikov degeneration. For a moduli of lattice-polarized K3s with a recognizable divisor we construct a canonical stable slc pair (KSBA) compactification and prove that it is semi toroidal. We prove that the rational curve divisor is recognizable, and give many other examples.

Host: Elham Izadi

### November 19, 2021

### 3:00 PM

### Contact Samir Canning at srcannin@ucsd.edu for zoom info.

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