Title：Fano 3-folds, Lagrangian fibrations and a supersingular OG10 with Co2 configuration

Abstract: Holomorphic symplectic manifolds appear as moduli of sheaves on K3 surfaces. In several cases, they acquire an intermediate Jacobian fibration structure of Fano-extensions of a fixed polarized K3 surface. After explaining the contact (g=10) and Legendrian (g=9) cases, I will apply the genus g=8 case to the construction of a Leech lattice analogue of a del Pezzo surface of degree 1.