A characterization of the family of secant lines to a hyperbolic quadric in PG(3,q), q odd

TL;DR

This paper provides a combinatorial description of secant lines to a hyperbolic quadric in PG(3,q), based on their intersection patterns with points and planes, enhancing understanding of geometric configurations in finite projective spaces.

Contribution

It offers a novel combinatorial characterization of secant lines to hyperbolic quadrics in PG(3,q), expanding geometric and algebraic insights in finite projective geometry.

Findings

Characterization of secant lines via intersection properties

Enhanced understanding of hyperbolic quadric line configurations

Framework applicable to finite projective spaces

Abstract

We give a combinatorial characterization of the family of lines of P G(3, q) which meet a hyperbolic quadric in two points (the so called secant lines) using their intersection properties with the points and planes of PG(3,q).