On $m$-ovoids of regular near polygons

TL;DR

This paper extends previous research on $m$-ovoids in dual polar spaces, demonstrating that nontrivial cases are hemisystems and providing a broader result applicable to regular near polygons.

Contribution

It generalizes earlier findings by showing nontrivial $m$-ovoids are hemisystems in specific dual polar spaces and extends the result to regular near polygons.

Findings

Nontrivial $m$-ovoids in certain dual polar spaces are hemisystems.

A more general theorem applies to regular near polygons.

The work unifies and extends previous classifications of $m$-ovoids.

Abstract

We generalise the work of Segre (1965), Cameron - Goethals - Seidel (1978), and Vanhove (2011) by showing that nontrivial $m$-ovoids of the dual polar spaces $DQ(2d, q)$, $DW(2d-1,q)$ and $DH(2d-1,q^2)$ ($d\ge 3$) are hemisystems. We also provide a more general result that holds for regular near polygons.