A New Infinite Family of Hemisystems of the Hermitian Surface

TL;DR

This paper introduces an infinite family of hemisystems for the Hermitian surface, expanding the known configurations and providing new algebraic structures for specific prime powers.

Contribution

It constructs an infinite family of hemisystems of the Hermitian surface for all odd prime powers congruent to 3 mod 4, with explicit automorphism groups.

Findings

Existence of hemisystems for all such prime powers

Construction admits automorphism group C_{(q^3+1)/4} : C_3

Advances understanding of geometric configurations in finite surfaces

Abstract

In this paper, we construct an infinite family of hemisystems of the Hermitian surface $\mathsf{H}(3,q^2)$. In particular, we show that for every odd prime power $q$ congruent to $3$ modulo $4$, there exists a hemisystem of $\mathsf{H}(3,q^2)$ admitting $C_{(q^3+1)/4} : C_3$.