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Restriction of stable bundles in characteristic $\protect {p}$

Author: Tohru Nakashima
Journal: Trans. Amer. Math. Soc. 349 (1997), 4775-4786
MSC (1991): Primary 14D20, 14F05
MathSciNet review: 1451612
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Abstract: Let $k$ be an algebraically closed field of characteristic $p>0$. Let $X$ be a nonsingular projective variety defined over $k$ and $H$ an ample line bundle on $X$. We shall prove that there exists an explicit number $m_{0}$ such that if $E$ is a $\mu $-stable vector bundle of rank at most three, then the restriction $E_{\vert D}$ is $\mu $-stable for all $m\geq m_{0}$ and all smooth irreducible divisors $D\in \vert mH\vert $. This result has implications to the geometry of the moduli space of $\mu $-stable bundles on a surface or a projective space.

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Tohru Nakashima
Affiliation: Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo, 192-03 Japan

Received by editor(s): April 30, 1996
Article copyright: © Copyright 1997 American Mathematical Society

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