##### Department of Mathematics,

University of California San Diego

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### Math 208: Seminar in Algebraic Geometry

## Dr. David Stapleton

#### University of Michigan

## Studying the birational geometry of complex Fano hypersurfaces via characteristic p

##### Abstract:

In the 90s Kollár proved non-rationality of many degrees and dimensions of complex Fano hypersurfaces by considering their degenerations modulo p and taking advantage of the surprising existence and positivity of differential forms on their reductions. In a series of papers with Chen, Church, and Ji, we have shown that these differential forms in characteristic p can give insight into many other aspects of the birational geometry of complex hypersurfaces: the degree of irrationality, rational endomorphisms, the birational automorphism group, and rational fibrations in low genus curves.

Host: James McKernan

### October 6, 2023

### 3:15 PM

APM 7321

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