On the existence of O'Nan configurations in Buekenhout unitals in PG(2,q^2)

TL;DR

This paper proves that all nonclassical ovoidal Buekenhout-Metz unitals in PG(2,q^2) contain O'Nan configurations, advancing understanding of their geometric properties.

Contribution

It establishes the existence of O'Nan configurations in all nonclassical ovoidal Buekenhout-Metz unitals, a previously unresolved question.

Findings

O'Nan configurations exist in all nonclassical ovoidal Buekenhout-Metz unitals

The result applies to all such unitals in PG(2,q^2)

Advances understanding of the structure of these unitals

Abstract

In this paper, we establish the existence of O'Nan configurations in all nonclassical ovoidal Buekenhout-Metz unitals in $\text{PG}(2,q^2)$.