Vanishing sequences and Okounkov bodies

Abstract

We define and study the vanishing sequence along a real valuation of sections of a line bundle on a projective variety. Building on previous work of the first author with Huayi Chen, we prove an equidistribution result for vanishing sequences of large powers of a big line bundle, and study the limit measure. In particular, the latter is described in terms of restricted volumes for divisorial valuations. We also show on an example that the associated concave function on the Okounkov body can be discontinuous at boundary points.

17 pages, supercedes the preprint arXiv:1210.3523. v2: 21 pages, expanded Section 2. Final version, to appear in Math. Ann

References in corpus (2)

• Okounkov bodies of filtered linear series
• Test configurations and Okounkov bodies

Cited by in corpus (5)

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• The volume of singular Kähler-Einstein Fano varieties
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• Seshadri-type constants and Newton-Okounkov bodies for non-positive at infinity valuations of Hirzebruch surfaces
• On the valuative Nagata conjecture