%0 Journal Article
%T Free pencils on divisors
%A Roberto Paoletti
%J Mathematics
%D 1993
%I arXiv
%X 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).
%U http://arxiv.org/abs/alg-geom/9303005v2