Positivity of Line Bundles and Newton-Okounkov Bodies

The purpose of this paper is to describe asymptotic base loci of line bundles on projective varieties in terms of Newton--Okounkov bodies. As a result, we obtain equivalent characterizations of ampleness and nefness via convex geometry.

2010 Mathematics Subject Classification: 14C20, 32Qxx, 52A20

Keywords and Phrases: positivity of line bundles, ampleness, augmented and restricted base loci, Newton--Okounkov bodies

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