Every flock generalised quadrangle has a hemisystem

TL;DR

This paper proves that all flock generalized quadrangles contain hemisystems and introduces a unifying construction method that encompasses previous classical examples.

Contribution

It establishes a universal property of flock generalized quadrangles and provides a new construction approach linking existing classical cases.

Findings

All flock generalized quadrangles contain hemisystems.

A unified construction method for these hemisystems.

Connections to classical examples by Cossidente and Penttila.

Abstract

We prove that every flock generalised quadrangle contains a hemisystem, and we provide a construction method which unifies our results with the examples of Cossidente and Penttila in the classical case.