Kodaira dimensions of some moduli spaces of hyperkähler fourfolds

Abstract: The Noether-Lefschetz locus in a moduli space of K3^[2]-fourfolds parametrizes fourfolds with Picard rank at least 2. Following Hassett’s work on cubic fourfolds, Debarre, Iliev, and Manivel showed that the Noether-Lefschetz locus in the moduli space of degree 2 K3^[2]-fourfolds is a countable union of special divisors indexed by discriminant d. In this talk, we compute the Kodaira dimensions of these special divisors for all but finitely many discriminants; in particular, we show the divisors for discriminants greater than 224 are all of general type.

algebraic geometry

Audience: researchers in the topic

Algebraic Geometry NorthEastern Series (AGNES)