Article ID Journal Published Year Pages File Type
6425654 Advances in Mathematics 2014 13 Pages PDF
Abstract
A holomorphic Lagrangian fibration on a holomorphically symplectic manifold is a holomorphic map with Lagrangian fibers. It is known (due to Huybrechts) that a given compact manifold admits only finitely many holomorphic symplectic structures, up to deformation. We prove that a given compact, simple hyperkähler manifold with b2⩾7 admits only finitely many deformation types of holomorphic Lagrangian fibrations. We also prove that all known hyperkähler manifolds are never Kobayashi hyperbolic.
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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