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Fano threefolds in positive characteristic

Published online by Cambridge University Press:  04 December 2007

N. I. SHEPHERD-BARRON
N. I. SHEPHERD-BARRON
Affiliation:
D.P.M.M.S., Cambridge University, 16 Mill Lane, Cambridge CB2 1SB, U.K.
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Abstract

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We show that the birational classification in positive characteristic of smooth Fano threefolds $X$ with Picard number 1 is the same as in characteristic zero. In particular, there are no exotic such Fanos; as a consequence of the classification, $X$ is shown to be liftable without ramification to characteristic zero and to contain a line. The main techniques employed are those of Ekedahl and of Mori and Takeuchi.

Keywords

Fano varietyprojectionflopextermal raysmonodromy
Type
Research Article
Information
Compositio Mathematica , Volume 105 , Issue 3 , February 1997 , pp. 237 - 265
Copyright
© 1997 Kluwer Academic Publishers