##### Department of Mathematics,

University of California San Diego

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### Algebraic Geometry Seminar

## Federico Buonerba

#### Courant Institute

## Lefschetz hyperplane theorems in Arakelov geometry

##### Abstract:

We will discuss Lefschetz theorems on the homotopy groups of hyperplane sections in the arithmetic setting, i.e. for a divisor, ample in the Arakelov sense, over a projective scheme defined over the ring of integers in a number field. An interesting corollary is that the integral model of a generic complete intersection curve of big height, is a simply connected arithmetic surface. Joint work with Michael McQuillan.

Host: James McKernan

### September 30, 2016

### 4:00 PM

### AP&M 5829

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