Abstract.
We classify singular fibres over general points of the discriminant locus of projective Lagrangian fibrations over 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 \(A_n, \tilde{A_n}\) or \(\tilde{D_n}\). Moreover, we show all types of the above singular fibres actually occur.
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Received: 10 March 2000 / Revised version: 29 September 2000 / Published online: 24 September 2001
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Matsushita, D. On singular fibres of Lagrangian fibrations over holomorphic symplectic manifolds. Math Ann 321, 755–773 (2001). https://doi.org/10.1007/s002080100251
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DOI: https://doi.org/10.1007/s002080100251