Prime Fano threefolds and integrable systems

Atanas Iliev (1) , Laurent Manivel (2)

1 Department of Mathematics
2 IF - Institut Fourier

For a general K3 surface $S$ of genus $g$, with $2 \le g \le 10$, we prove that the intermediate Jacobians of the family of prime Fano threefolds of genus $g$ containing $S$ as a hyperplane section, form generically an algebraic completely integrable Hamiltonian system.

Mots clés: Fano threefold; K3 surface; integrable system; intermediate jacobian

Domaines: Géométrie algébrique [math.AG]

Atanas Iliev, Laurent Manivel. Prime Fano threefolds and integrable systems. Mathematische Annalen, 2007, 339 (4), pp.937-955. ⟨hal-00330601⟩