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In the definition of irreducible holomorphic symplectic manifolds thecondition of being simply connected can be replaced by vanishing irregularity.We discuss finite quotients X of complex tori where the space of reflexive2-forms is generated by a holomorphic symplectic form, and their Lagrangianfibrations. Neither X nor the base can be smooth unless X is a 2-torus.

On the definition of irreducible holomorphic symplectic manifolds and their singular analogs