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arXiv · 1911.03435

Kodaira dimension of moduli of special $K3^{[2]}$-fourfolds of degree 2

Jack Petok
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Abstract

We study the Noether-Lefschetz locus of the moduli space $\mathcal{M}$ of $K3^{[2]}$-fourfolds with a polarization of degree $2$. Following Hassett's work on cubic fourfolds, Debarre, Iliev, and Manivel have shown that the Noether-Lefschetz locus in $\mathcal{M}$ is a countable union of special divisors $\mathcal{M}_d$, where the discriminant $d$ is a positive integer congruent to $0,2,$ or $4$ modulo 8. We compute the Kodaira dimensions of these special divisors for all but finitely many discriminants; in particular, we show that for $d>224$ and for many other small values of $d$, the space $\mathcal{M}_d$ is a variety of general type.

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Jack Petok. 2019-11-08. Kodaira dimension of moduli of special $K3^{[2]}$-fourfolds of degree 2. https://arxiv.org/abs/1911.03435

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