Vector bundles on Fano threefolds and K3 surfaces

Arnaud Beauville (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

Let X be a Fano threefold, and let S be a K3 surface in X . Any moduli space M of simple vector bundles on S carries a holomorphic symplectic structure. Following an idea of Tyurin, we show that in some cases, those vector bundles which come from X form a Lagrangian subvariety of M . We illustrate this with a number of concrete examples.

Domaines: Géométrie algébrique [math.AG]

Arnaud Beauville. Vector bundles on Fano threefolds and K3 surfaces. Bollettino dell'Unione Matematica Italiana. B, 2022, 15 (1-2), pp.43-55. ⟨10.1007/s40574-020-00266-1⟩. ⟨hal-02509876⟩