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arXiv · 2604.06851

A symplectic fourfold

Maria Donten-Bury·Grzegorz Kapustka·Benedetta Piroddi·Tomasz Wawak
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Abstract

We present a method to construct irreducible symplectic varieties by studying terminalisations of quotient of hyper-K\"ahler manifolds by non-natural group actions. In particular, we construct irreducible symplectic varieties of dimension $4$ with $b_2 = 4$ and non-quotient singularities: this provides explicit examples of ISVs for which a global Torelli theorem is not known to hold.

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Maria Donten-Bury, Grzegorz Kapustka, Benedetta Piroddi, Tomasz Wawak. 2026-04-08. A symplectic fourfold. https://arxiv.org/abs/2604.06851

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