Weighted Intriguing Sets in Finite Polar Spaces

TL;DR

This paper presents new proofs and improved results regarding the non-existence of ovoids in certain finite polar spaces, advancing understanding in finite geometry and polar space theory.

Contribution

It offers novel proofs for ovoid non-existence in hyperbolic spaces of rank ≥4 and Hermitian spaces, and enhances previous non-existence results by Klein.

Findings

Proved non-existence of ovoids in hyperbolic spaces of rank ≥4 in even characteristic

Established non-existence of ovoids in Hermitian polar space H(5,4)

Improved bounds on ovoid existence in Hermitian and hyperbolic quadrics

Abstract

We provide new proofs for the non-existence of ovoids in hyperbolic spaces of rank at least four in even characteristic, and for the Hermitian polar space $\mathsf{H}(5, 4)$. We also improve the results of A. Klein on the non-existence of ovoids of Hermitian spaces and hyperbolic quadrics.