%0 Journal Article
%T Ample vector bundles and intrinsic quadric fibrations over irrational curves
%A Tommaso De Fernex
%J Le Matematiche
%D 2000
%I University of Catania
%X Let E be an ample vector bundle of rank r ¡Ý 2 on a smooth complex projective variety X.  This work is part of the following problem: to study and classify the pair (X, E) assuming the existence of a regular section s ¡Ê¦£ (X, E) whose zero locus is a special subvariety of X . In [2] and [11], the case of Z quadric fibration, respectively of diimension 2 or more, over a smooth curve is discussed under the further hypothesis that the quadric fibration structure is induced on Z by an ample line bundle L on X . Here the same situation is considered, and classification is given assuming the base curve to be irrational, in the more general case that the quadric fibration structure of Z is intrinsic, i.e. not a priori induced by a polarization of X .
%K Ample vector bundle
%K Quadric fibration
%K Polarization
%K Cone of curves
%U http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/268