Complex ball quotients from manifolds of $K3^{[n]}$ -type

preprint2015arXivOpen access

We describe periods of irreducible holomorphic manifolds of $K3^{[n]}$ -type with a non-symplectic automorphism of prime order $p\geq 3$ . These turn out to lie on complex ball quotients and we are able to give a precise characterization of when the period map is bijective, by introducing the notion of $K(T)$ -generality.

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Complex ball quotients from manifolds of $K3^{[n]}$ -type

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Complex ball quotients from manifolds of K3[n]K3^{[n]}K3[n]-type

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Complex ball quotients from manifolds of $K3^{[n]}$ -type