Abstract:
Let $X$ be a Fano threefold, and let $S \subset X$ be a smooth anticanonical
surface (hence a K3). Any moduli space $\mathcal{M}_S$ 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 $\mathcal{M}_S$. Most of the talk
will be devoted to concrete examples of this situation.
