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\(k\)-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.

MSC:

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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References:

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