Семинар лаборатории алгебраической геометрии: Михаил Вербицкий

Аннотация: A special Kahler manifold is a Kahler manifold (I,g,w) equipped with a symplectic flat torsion-free connection such that the metric g is locally the Hessian of a function. This geometry naturally occurs on the base of a holomorphic Lagrangian fibration. Total space of a cotangent bundle to a special Kahler manifold is hyperkahler. Let Z\subset M be a Lagrangian subvariety of a holomorphic symplectic manifold equipped with a Lagrangian fibration \pi: M \arrow B. We prove that \pi(Z) is a special Kahler
subvariety in B. This answers a question of N. Hitchin related to Kapustin-Witten BBB/BAA duality. This is a joint work with Ljudmila Kamenova.