%0 Journal Article
%T Numerical Criteria for vey Ampleness of Divisors on Projective Bundles over an elliptic curve
%A Alberto Alzati
%A Marina Bertolini
%A Gian Mario Besana
%J Mathematics
%D 1997
%I arXiv
%X In Butler, J.Differential Geom. 39 (1):1--34,1994, the author gives a sufficient condition for a line bundle associated with a divisor D to be normally generated on $X=P(E)$ where E is a vector bundle over a smooth curve C. A line bundle which is ample and normally generated is automatically very ample. Therefore the condition found in Butler's work, together with Miyaoka's well known ampleness criterion, give a sufficient condition for the very ampleness of D on X. This work is devoted to the study of numerical criteria for very ampleness of divisors D which do not satisfy the above criterion, in the case of C elliptic. Numerical conditions for the very ampleness of D are proved,improving existing results. In some cases a complete numerical characterization is found.
%U http://arxiv.org/abs/alg-geom/9702013v1