On Unirationality of Quartics over non Algebraically Closed Fields

TL;DR

This paper presents examples of smooth quartic hypersurfaces over non algebraically closed fields that are unirational without relying on linear spaces, expanding understanding of unirationality in algebraic geometry.

Contribution

It introduces a novel method for establishing unirationality of quartics over non algebraically closed fields that does not depend on linear spaces.

Findings

Examples of smooth unirational quartics over non algebraically closed fields

Unirationality proven without linear space existence on quartics

New approach broadens methods for studying quartic hypersurfaces

Abstract

We give examples of smooth $\k$-unirational line-free quartic hypersurfaces over a non algebraically closed field $\k$. Unlike other methods of proving unirationality, our method does not rely on existence of linear spaces on quartics.