Universal families of Gushel-Mukai fourfolds

Abstract

We define universal Gushel-Mukai fourfolds over certain $\textit{Noether-Lefschetz}$ loci in the moduli stack of Gushel-Mukai fourfolds $\mathcal{M}^4_{GM}$. Using the relation between these fourfolds and K3 surfaces, we relate moduli of K3 surfaces to universal Gushel-Mukai varieties, and their birational geometry. This allows us to prove the unirationality or rationality of some of these universal families.Comment: 13 page