## 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

Topics: Mathematics - Algebraic Geometry
Year: 2020
OAI identifier: oai:arXiv.org:2009.11770

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