Jun-Muk Hwang, KIAS, Korea

Webs of Lagrangian tori in projective symplectic manifolds

Abstract

Given a Lagrangian torus A in a projective irreducible symplectic manifold M, Beauville raised the question whether some birational model of M admits a fibration with A as a fiber. In a joint work with Richard Weiss, we give an affirmative answer. Our work employs two different tools: the theory of action-angle variables for algebraically completely integrable Hamiltonian systems and Wielandt's theory of subnormal subgroups. To apply these tools, we will introduc the notion of webs of submanfiolds and study their monodromy groups.