Ekaterina Amerik (Orsay and HSE, Moscow) will speak in the geometry seminar on the 15th November, at 11am. Her title is “On the characteristic foliation on a smooth divisor in a holomorphic symplectic manifold” and her abstract can be found below. The talk will take place at 11am in the Salle de Profs, on the 9th floor of building NO.
Let D be a smooth hypersurface in a holomorphic symplectic manifold. The kernel of the restriction of the symplectic form on D defines a foliation in curves, called the characterisic foliation. Hwang and Viehweg proved in 2008 that if D is of general type this foliation cannot be algebraic unless in the trivial case when X is a surface and D is a curve. I shall explain a refinement of this result, joint with F. Campana: the characteristic foliation is algebraic if and only if D is uniruled or a finite covering of X is a product with a symplectic surface and D comes from a curve on that surface. I shall also explain a recent joint work with L. Guseva, concerning the particular case of an irreducible holomorphic symplectic fourfold: we show that if Zariski closure of a general leaf is a surface, then X is a lagrangian fibration and D is the inverse image of a curve on its base.