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arXiv · 2212.12586

Kodaira dimension of moduli spaces of hyperkähler varieties

Ignacio Barros·Pietro Beri·Emma Brakkee·Laure Flapan
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Abstract

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.

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BibTeXRIS

Ignacio Barros, Pietro Beri, Emma Brakkee, Laure Flapan. 2024-09-10. Kodaira dimension of moduli spaces of hyperkähler varieties. https://arxiv.org/abs/2212.12586

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