Numerical Criteria for vey Ampleness of Divisors on Projective Bundles over an elliptic curve

Details Numerical Criteria for vey Ampleness of Divisors on Projective Bundles over an elliptic curve Numerical Criteria for vey Ampleness of Divisors on Projective Bundles over an elliptic curve

1997-02-20

arxiv.org/abs/alg-geom/9702013v1

Mathematics

Algebraic Geometry

AMS-Latex, 18 pages, Canadian Journal of Math, Dec 1996

Scientific paper

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.

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