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

2019/11/08 by Petok, Jack
#14J32 #14J35 #32N15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Primary 14J15 #Secondary 32M15

paper · doi:10.48550/arxiv.1911.03435

Abstract

We study the Noether-Lefschetz locus of the moduli space 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 M is a countable union of special divisors 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 M_d is a variety of general type.

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