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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References
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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