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Title:
Holomorphic Lagrangian subvarieties, Lagrangian fibrations and special Kahler geometry
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Abstract:
Let $M$ be a holomorphic symplectic Kahler manifold equipped with a Lagrangian fibration with compact fibers. The base of this manifold is equipped with a special Kahler structure, that is, a Kahler structure $(I, g, \omega)$ and a symplectic flat torsion-free connection such that the metric $g$ is locally the Hessian of a function. We prove that any Lagrangian subvariety $Z\subset M$ which intersects smooth fibers of $\pi$ is a toric fibration over its image $\pi(Z)$ in $B$, and this image is also special Kahler.
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