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Geometria Diferencial

Lagrangian fibrations and special Kahler geometry
Misha Verbitsky

Terça-feira, 11 de junho de 2019, 15:30
Sala 236.

A special Kahler manifold is a Kahler manifold $(I, g, \omega)$ 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 $\pi:M \mapsto B$. 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.