# Vector bundles on Fano threefolds and $K3$ surfaces – Arnaud Beauville (Université Côte d’Azur, Nice)

#### Venue

Dipartimento di Matematica, Aula Magna.

#### Abstract

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.

Further information is available on the event page on the Indico platform.

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