Regular pairs of quadratic forms on odd-dimensional spaces in characteristic 2

TL;DR

This paper establishes a normal form for smooth intersections of two quadrics in even-dimensional projective spaces over fields of characteristic 2, and explores automorphisms and rational points on related algebraic varieties.

Contribution

It introduces a normal form for such intersections and characterizes their automorphism groups, with applications to rational points on quartic del Pezzo surfaces.

Findings

Normal form for smooth intersections of two quadrics in characteristic 2

Automorphism group descriptions for these varieties

Existence of canonical rational points on quartic del Pezzo surfaces

Abstract

We describe a normal form for a smooth intersection of two quadrics in even-dimensional projective space over an arbitrary field of characteristic 2. We use this to obtain a description of the automorphism group of such a variety. As an application, we show that every quartic del Pezzo surface over a perfect field of characteristic 2 has a canonical rational point and, thus, is unirational.