\(k\)-very ample line bundles on Del Pezzo surfaces. (English) Zbl 0870.14031

The paper makes a detailed study of line bundles on Del Pezzo surfaces. It includes numerical determinations of: the divisors with \(D^2=0\); nef divisors; \(k\)-very ample line bundles. In particular it concludes that a line bundle is nef if and only if it is spanned by its global sections and ample if and only if it is very ample.


14J70 Hypersurfaces and algebraic geometry
14C20 Divisors, linear systems, invertible sheaves
14J25 Special surfaces
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
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