Vanishing sequences and Okounkov bodies

Sébastien, Boucksom and Küronya, Alex and Catriona, Maclean and Tomasz, Szemberg (2015) Vanishing sequences and Okounkov bodies. MATHEMATISCHE ANNALEN, 361 (3-4). pp. 811-834. ISSN 0025-5831

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Abstract

We define and study the vanishing sequence along a real valuation of sections of a line bundle on a normal 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.

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