Irreducible symplectic varieties with a large second Betti number

Yuchen Liu; Zhiyu Liu; Chenyang Xu

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arXiv · 2410.01566

Irreducible symplectic varieties with a large second Betti number

Yuchen Liu·Zhiyu Liu·Chenyang Xu

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Abstract

We prove a general result on the existence of irreducible symplectic compactifications of non-compact Lagrangian fibrations. As an application, we show that the relative Jacobian fibration of cubic fivefolds containing a fixed cubic fourfold can be compactified by a $\mathbb{Q}$-factorial terminal irreducible symplectic variety with the second Betti number at least 24, and admits a Lagrangian fibration whose base is a weighted projective space. In particular, it belongs to a new deformation type of irreducible symplectic varieties.

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Yuchen Liu, Zhiyu Liu, Chenyang Xu. 2024-10-02. Irreducible symplectic varieties with a large second Betti number. https://arxiv.org/abs/2410.01566

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