Skip to Main Content
Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Birational geometry of quadrics in characteristic $2$

Author: Burt Totaro
Journal: J. Algebraic Geom. 17 (2008), 577-597
Published electronically: March 13, 2008
MathSciNet review: 2395138
Full-text PDF

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 $2$.

References [Enhancements On Off] (What's this?)


Additional Information

Burt Totaro
Affiliation: DPMMS, Wilberforce Road, Cambridge CB3 0WB, England
MR Author ID: 272212

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