Birational geometry of quadrics in characteristic 2

Totaro, Burt

doi:10.1090/S1056-3911-08-00472-4

Birational geometry of quadrics in characteristic $2$

Author: Burt Totaro
Journal: J. Algebraic Geom. 17 (2008), 577-597
DOI: https://doi.org/10.1090/S1056-3911-08-00472-4
Published electronically: March 13, 2008
MathSciNet review: 2395138
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Abstract | References | Additional Information

Abstract: A conic bundle or quadric bundle in characteristic $2$ can have generic fiber which is nowhere smooth over the function field of the base variety; in that case, the generic fiber is called a quasilinear quadric. We solve some of the main problems of birational geometry for quasilinear quadrics, which remain open for quadrics in characteristic not $2$: when are two quadrics birational, and when is a quadric ruled over the base field? The proofs begin by extending Karpenko and Merkurjev’s theorem on the essential dimension of quadrics to arbitrary quadrics (smooth or not) in characteristic $2$.

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Additional Information

Burt Totaro
Affiliation: DPMMS, Wilberforce Road, Cambridge CB3 0WB, England
MR Author ID: 272212
Email: b.totaro@dpmms.cam.ac.uk

Received by editor(s): August 13, 2006
Received by editor(s) in revised form: November 1, 2006
Published electronically: March 13, 2008