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- W2949275276 abstract "Let X be a smooth projective variety defined over an algebraically closed field, and let Y in X be a reduced and irreducible ample divisor in X. We give a numerical sufficient condition for a base point free pencil on $Y$ to be the restriction of a base point free pencil on $X$. This result is then extended to families of pencils and to morphisms to arbitrary smooth curves. Serrano had already studied this problem in the case n=2 and 3, and Reider had then attacked it in the case $n=2$ using vector bundle methods based on Bogomolov's instability theorem on a surface (char(k)=0). The argument given here is based on Bogomolov's theorem on an n-dimensional variety, and on its recent adaptations to the setting of prime charachterstic (due to Shepherd-Barron and Moriwaki)." @default.
- W2949275276 created "2019-06-27" @default.
- W2949275276 creator A5086415185 @default.
- W2949275276 date "1993-03-28" @default.
- W2949275276 modified "2023-09-27" @default.
- W2949275276 title "Free pencils on divisors" @default.
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