Intersections of the Hermitian Surface with irreducible Quadrics in even Characteristic

TL;DR

This paper classifies the possible intersection sizes between Hermitian surfaces and irreducible quadrics in projective 3-space over finite fields of even characteristic, focusing on cases sharing a tangent plane at a non-singular point.

Contribution

It provides a complete characterization of intersection sizes for Hermitian surfaces and irreducible quadrics in even characteristic, a case not fully explored before.

Findings

Identifies all possible intersection sizes under given conditions

Provides explicit descriptions for intersection configurations

Enhances understanding of geometric structures in finite projective spaces

Abstract

We determine the possible intersection sizes of a Hermitian surface $\mathcal H$ with an irreducible quadric of ${\mathrm PG}(3,q^2)$ sharing at least a tangent plane at a common non-singular point when $q$ is even.