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

Dolgachev, Igor; Duncan, Alexander

doi:10.2140/ant.2018.12.99

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

Igor Dolgachev and Alexander Duncan

Vol. 12 (2018), No. 1, 99–130

DOI: 10.2140/ant.2018.12.99

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

Vol. 12, No. 1, 2018