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On singular fibres of complex Lagrangian fibrations

Daisuke Matsushita
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Abstract

We classify singular fibres over general points of the discriminant locus of projective complex Lagrangian fibrations on 4-dimensional holomorphic symplectic manifolds. The singular fibre F is the following either one: F is isomorphic to the product of an elliptic curve and a Kodaira singular fibre up to finite unramified covering or F is a normal crossing variety consisting of several copies of a minimal elliptic ruled surface of which the dual graph is Dynkin diagram of type A_n, $\tilde{A_n}$, $\tilde{D_n}$ or D_n.

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Daisuke Matsushita. 1999-11-22. On singular fibres of complex Lagrangian fibrations. https://arxiv.org/abs/math/9911164

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