The unirationality of the moduli space of K3 surfaces of genus 22

TL;DR

This paper proves that the moduli space of polarized K3 surfaces of genus 22 is unirational by leveraging a connection with special cubic fourfolds, advancing understanding of the geometry of these moduli spaces.

Contribution

It establishes the unirationality of the moduli space of genus 22 K3 surfaces using a novel link with special cubic fourfolds and their Noether-Lefschetz loci.

Findings

The universal K3 surface over F_{22} is unirational.

A new connection between cubic fourfolds and K3 surfaces of genus 22 is utilized.

The result advances the classification of moduli spaces of K3 surfaces.

Abstract

Using the connection discovered by Hassett between the Noether-Lefschetz moduli space of special cubic fourfolds of discriminant 42 and the moduli space F_{22} of polarized K3 surfaces of genus 22, we show that the universal K3 surface over F_{22} is unirational.