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arXiv · 1403.5523

A singular symplectic variety of dimension 6 with a Lagrangian Prymian fibration

Tommaso Matteini
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Abstract

A projective symplectic variety $\mathcal{P}$ of dimension 6, with only finite quotient singularities, $\pi(\mathcal{P})=0$ and $h^{(2,0)}(\mathcal{P}_{smooth})=1$, is described as a relative compactified Prym variety of a family of genus 4 curves with involution. It is a Lagrangian fibration associated to a K3 surface double cover of a generic cubic surface. It has no symplectic desingularization.

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Tommaso Matteini. 2014-03-21. A singular symplectic variety of dimension 6 with a Lagrangian Prymian fibration. https://arxiv.org/abs/1403.5523

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