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
DOI: https://doi.org/10.1090/S1056-3911-08-00472-4
Published electronically: March 13, 2008
MathSciNet review: 2395138
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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
Email: b.totaro@dpmms.cam.ac.uk

DOI: https://doi.org/10.1090/S1056-3911-08-00472-4
Received by editor(s): August 13, 2006
Received by editor(s) in revised form: November 1, 2006
Published electronically: March 13, 2008

American Mathematical Society