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Justin Sawon: Lectures

September 10, 2023
TITLE: Lagrangian fibrations in four and six dimensions

ABSTRACT: We consider Lagrangian fibrations by abelian surfaces and threefolds over the complex projective plane and threespace, respectively, with total space holomorphic symplectic manifolds or varieties. We recall some classification results of Markushevich, Kamenova, and the speaker in the principally polarized case, and a new classification result in the (1,2) polarized case (joint work with Xuqiang Qin). We also describe restrictions on the polarization; indeed, `most’ polarizations are not possible.

Recorded June 2020
TITLE: Singular fibres of holomorphic Lagrangian fibrations

ABSTRACT: Fibrations on compact holomorphic symplectic manifolds are Lagrangian: their fibres must be Lagrangian with respect to the holomorphic symplectic structure. Moreover, the general fibre must be an abelian variety and singular fibres must occur in codimension one. In this talk I will survey results of Matsushita, Hwang-Oguiso, Christian Lehn, and myself that describe the structure of the singular fibres that can occur in these Lagrangian fibrations.
Slides of Lecture