k-very ample line bundles on Del Pezzo Surfaces

Details k-very ample line bundles on Del Pezzo Surfaces k-very ample line bundles on Del Pezzo Surfaces

1995-02-15

arxiv.org/abs/alg-geom/9502012v1

Mathematics

Algebraic Geometry

AMSLATEX file, 10 pages. To appear on Math. Nachrt

Scientific paper

A $k$-very ample line bundle L on a Del Pezzo Surface is numerically characterized. We find that the set of the exceptional curves and effective divisors with selfintersection zero, $\cal S$, plays a very important rule in checking the nefness and $k$-very ampleness of a line bundle on a Del pezzo Surface. We show that a line bundle L is nef if and only if it is spanned and that L is $k$-very ample if and only if the intersection with all the elements of $\cal S$ is greater or equal than k. In the first part of the paper we give a complete numerical description of the elements of $\cal S$ .

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