k-very ample line bundles on Del Pezzo Surfaces

Abstract

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, $\mathcal{S}$, 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 $\mathcal{S}$ is greater or equal than k. In the first part of the paper we give a complete numerical description of the elements of $\mathcal{S}$ .

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

Cited by in corpus (1)

• Stable maps to Looijenga pairs