A symplectic fourfold
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 b2 = 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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