Newton-Okounkov bodies sprouting on the valuative tree

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

Newton-Okounkov bodies sprouting on the valuative tree

Algebraic Geometry 2016-02-08 v1

Authors: C. Ciliberto , M. Farnik , A. Küronya , V. Lozovanu , J. Roé , C. Shramov

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.

Keywords

Newton-Okounkov body valuative tree smooth projective surface big divisor valuation infinitely near flag infinitesimal variation

Cite

@article{arxiv.1602.02074,
  title  = {Newton-Okounkov bodies sprouting on the valuative tree},
  author = {C. Ciliberto and M. Farnik and A. Küronya and V. Lozovanu and J. Roé and C. Shramov},
  journal= {arXiv preprint arXiv:1602.02074},
  year   = {2016}
}

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33 pages, 3 figures

Newton-Okounkov bodies sprouting on the valuative tree

Abstract

Keywords

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