##### Department of Mathematics,

University of California San Diego

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### Math 208 - Algebraic Geometry Seminar

## Justin Lacini

#### UCSD

## Log Del Pezzo surfaces in positive characteristic

##### Abstract:

A log Del Pezzo surface is a normal log terminal surface with anti-ample canonical bundle. Over the complex numbers, Keel and McKernan have classified all but a bounded family of the simply connected log Del Pezzo surfaces of rank one. In this talk we extend their classification in positive characteristic, and in particular we prove that for $p>5$ every log Del Pezzo surface of rank one lifts to characteristic zero with smooth base. As a consequence, we see that Kawamata-Viehweg vanishing holds in this setting. Finally, we exhibit some counter-examples in characteristic two, three and five.

### November 16, 2018

### 1:00 PM

### AP&M 5829

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