Vol. 12, No. 1, 2018

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Regular pairs of quadratic forms on odd-dimensional spaces in characteristic 2

Igor Dolgachev and Alexander Duncan

Vol. 12 (2018), No. 1, 99–130
Abstract

We describe a normal form for a smooth intersection of two quadrics in even-dimensional projective spaces 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.

Keywords
quadratic forms, characteristic 2, quadrics
Mathematical Subject Classification 2010
Primary: 11E04
Secondary: 14C21, 14G17
Milestones
Received: 1 February 2017
Revised: 18 September 2017
Accepted: 8 November 2017
Published: 13 March 2018
Authors
Igor Dolgachev
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States
Alexander Duncan
Department of Mathematics
University of South Carolina
Columbia, SC
United States