Constructs irreducible symplectic varieties of dimension 2n (2≤n≤10) with 16≤b2≤24 as non-trivial terminalisations of finite symplectic quotients of Beauville-Mukai systems on very general K3-del Pezzo double covers.
A symplectic fourfold
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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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2026 1verdicts
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Irreducible symplectic varieties via K3-del Pezzo double covers
Constructs irreducible symplectic varieties of dimension 2n (2≤n≤10) with 16≤b2≤24 as non-trivial terminalisations of finite symplectic quotients of Beauville-Mukai systems on very general K3-del Pezzo double covers.