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A remark on semi-stable fibrations over $P^1$ in positive characteristic

Published online by Cambridge University Press:  04 December 2007

Khac VIET NGUYEN
Affiliation:
Institute of Mathematics, P.O. Box 631 BoHo, 10000 Hanoi, Vietnam; e-mail: nkviet@thevinh.ac.vn
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Abstract

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We prove a lower bound for the number of singular fibres of a non-isotrivial semi-stable family of curves over the projective line, in positive characteristic. The result is the same obtained previously by Beauville in characteristic zero, namely that the number is at least 4. Furthermore some consequences are discussed in the case that the number is exactly 4.

Type
Research Article
Copyright
© 1998 Kluwer Academic Publishers