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

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

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2017 University Press, Inc.
AMS Website