Characteristic foliation on the discriminantal hypersurface of a holomorphic Lagrangian fibration

Details Characteristic foliation on the discriminantal hypersurface of a holomorphic Lagrangian fibration Characteristic foliation on the discriminantal hypersurface of a holomorphic Lagrangian fibration

2007-10-12

arxiv.org/abs/0710.2376v1

Mathematics

Algebraic Geometry

Scientific paper

We give a Kodaira-type classification of general singular fibers of a holomorphic Lagrangian fibration in Fujiki's class $\mathcal C$. Our approach is based on the study of the characteristic vector field of the discriminantal hypersurface, which naturally arises from the defining equation of the hypersurface via the symplectic form. As an application, we show that the characteristic foliation of the discriminantal hypersurface has algebraic leaves which are either rational curves or smooth elliptic curves.

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