Kodaira dimension of moduli spaces of hyperkähler varieties

Barros, I.; Beri, P.; Brakkee, E.; Flapan, L.

doi:doi:10.14231/AG-2026-005

Persistent URL of this record https://hdl.handle.net/1887/4306972

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Faculty of Science: Other

Barros, I.; Beri, P.; Brakkee, E.; Flapan, L. (2026)

Kodaira dimension of moduli spaces of hyperkähler varieties

Article / Letter to editor

We study the Kodaira dimension of moduli spaces of polarized hyperkähler varieties deformation equivalent to the Hilbert scheme of points on a K3 surface or to O'Grady's ten dimensional variety. This question was studied by Gritsenko-Hulek-Sankaran in the cases of K3[2] and OG10 type when the divisibility of the polarization is one. We generalize their results to higher dimension and divisibility. As a main result, for almost all dimensions 2n we provide a lower bound on the degree such that for all higher degrees, every component of the moduli space of polarized hyperkähler varieties of K3[n] type is of general type.