Algebraic and Arithmetic Geometry Seminar

# Vector bundles on Fano threefolds and $K3$ surfaces

## by Arnaud Beauville (Université Côte d'Azur, Nice)

Europe/Rome
Aula Magna (Dipartimento di Matematica)

### Aula Magna

#### Dipartimento di Matematica

Description

Let $X$ be a Fano threefold, and let $S$ be a smooth anticanonical surface (hence a $K3$) lying in $X$. Any moduli space of simple vector bundles on $S$ carries a holomorphic symplectic structure. Following an idea of Tyurin, I will show that in some cases those vector bundles which come from $X$ form a Lagrangian subvariety of the moduli space. Most of the talk will be devoted to concrete examples of this situation.