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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