Seshadri constants and very ample divisors on algebraic surfaces

Abstract

A broadly applicable geometric approach for constructing nef divisors on blow ups of algebraic surfaces at n general points is given; it works for all surfaces in all characteristics for any n. This construction is used to obtain substantial improvements for currently known lower bounds for n point Seshadri constants. Remarks are included about a range of applications to classical problems involving linear systems on P2.

18 pages, plainTeX; reasons for replacement: Improved comparisons (Prop. I.2, Cor III.5), improved results in special cases (Prop. I.3, Lemma IV.6, Ex. IV.7), two additional citations, updated citations, and slight changes to Introduction