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

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.

35 pages; v2: introduction expanded with some new theorems

References in corpus (2)

• Maximal linear spaces contained in the base loci of pencils of quadrics
• Sheaf theoretic classifications of pairs of square matrices over arbitrary fields

Cited by in corpus (2)

• Quadratic points on intersections of two quadrics
• Strength conditions, small subalgebras, and Stillman bounds in degree $\le 4$