K3 Surfaces Of Genus 14 via Cubic Fourfolds

In a celebrated series of papers, Mukai established structure theorems for polarized K3 surfaces of all genera g<21, with the exception of the case g=14. Using Hassett's identification between the moduli space of polarized K3 surfaces of genus 14 and the moduli space of special cubic fourfolds of discriminant 26, we establish the rationality of the universal K3 surface of genus 14. The proof relies on a degenerate version of Mukai's structure theorem for K3 surfaces of genus 8. This is joint work with Verra.