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arXiv · 1602.02074

Newton-Okounkov bodies sprouting on the valuative tree

C. Ciliberto·M. Farnik·A. Küronya·V. Lozovanu·J. Roé·C. Shramov
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Abstract

Given a smooth projective algebraic surface X, a point O in X and a big divisor D on X, we consider the set of all Newton-Okounkov bodies of D with respect to valuations of the field of rational functions of X centred at O, or, equivalently, with respect to a flag (E,p) which is infinitely near to O, in the sense that there is a sequence of blowups mapping the smooth, irreducible rational curve E to O. The main objective of this paper is to start a systematic study of the variation of these infinitesimal Newton-Okounkov bodies as (E, p) varies, focusing on the case X = P2.

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C. Ciliberto, M. Farnik, A. Küronya, V. Lozovanu, J. Roé, C. Shramov. 2016-02-05. Newton-Okounkov bodies sprouting on the valuative tree. https://arxiv.org/abs/1602.02074

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