Unirationality of RDP Del Pezzo surfaces of degree 2

TL;DR

This paper investigates the conditions under which degree two Del Pezzo surfaces with rational double points are unirational over various fields, providing criteria based on field size and rational point density.

Contribution

It establishes new criteria for the unirationality of RDP Del Pezzo surfaces of degree two over different types of fields, extending previous understanding.

Findings

Unirational over finite fields with at least nine elements.

Unirational over infinite fields if and only if rational points are Zariski dense.

Provides conditions linking rational points and unirationality.

Abstract

We study unirationality of a Del Pezzo surface of degree two over a given (non algebraically closed) field, under the assumption that it admits at least one rational double point over an algebraic closure of the base field. As corollaries of our main results, we find that over a finite field, it is unirational if the cardinality of the field is greater than or equal to nine and we also find that over an infinite field, which is not necessarily perfect, it is unirational if and only if the rational points are Zariski dense over the field.