The universal K3 surface of genus 14 via cubic fourfolds

TL;DR

This paper proves the rationality of the universal K3 surface of genus 14 by linking it to special cubic fourfolds and employing a degenerate Mukai structure theorem, advancing understanding of moduli spaces and algebraic geometry.

Contribution

It establishes the rationality of the universal K3 surface of genus 14 via a novel approach connecting cubic fourfolds and nodal scrolls.

Findings

Universal K3 surface of genus 14 is rational

Established isomorphism with special cubic fourfolds of discriminant 26

Proved rationality using degenerate Mukai's theorem

Abstract

Using the isomorphism 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. Precisely, we show that the universal K3 surface of genus 14 is a projective bundle over a certain moduli space of nodal scrolls in P^5, whose rationality we prove using a degenerate version of Mukai's structure theorem for curves of genus 8.