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

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.
17 pages. Final version, to appear in Mathematische Annalen