##### Department of Mathematics,

University of California San Diego

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### Final Defense

## Iacopo Brivio

#### UCSD

## Invariance of plurigenera in positive and mixed characteristic

##### Abstract:

Over the complex numbers, a famous theorem of Siu states that the plurigenera $P_m$ of projective manifolds are invariant under deformations. We give examples of families of elliptic surfaces over a DVR of positive or mixed characteristic such that $P_m$ fails to be constant for all sufficiently divisible $m\geq 0$. Time permitting, we will show that (asymptotic) invariance of plurigenera holds for families of quasi-elliptic surfaces.

Advisor: James McKernan

### May 14, 2020

### 1:30 PM

### Zoom (contact Iacopo Brivio or James Mckernan)

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