Unirational Surfaces on the Noether Line

TL;DR

This paper demonstrates that simply connected surfaces of general type often exhibit unirationality, especially in positive characteristic, by constructing numerous unirational Horikawa surfaces.

Contribution

It introduces a method to construct many unirational Horikawa surfaces, highlighting the prevalence of unirationality among certain algebraic surfaces.

Findings

Unirationality is common among simply connected surfaces of general type.

Constructs numerous examples of unirational Horikawa surfaces.

Unirationality persists even in positive characteristic and fixed invariants.

Abstract

We show that among simply connected surfaces of general type unirationality is a common feature, even when fixing the positive characteristic or numerical invariants. To do so, we construct unirational Horikawa surfaces in abundance.