Newton–Okounkov bodies sprouting on the valuative tree

Given a smooth projective algebraic surface X , a point O ∈ 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 ne...

Full description

Saved in:
Bibliographic Details
Published in:Rendiconti del Circolo matematico di Palermo 2017-08, Vol.66 (2), p.161-194
Main Authors: Ciliberto, Ciro, Farnik, Michal, Küronya, Alex, Lozovanu, Victor, Roé, Joaquim, Shramov, Constantin
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematical analysis
Mathematics
Mathematics and Statistics
Rational functions
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Given a smooth projective algebraic surface X , a point O ∈ 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 O , in the sense that there is a sequence of blowups X ′ → X , mapping the smooth, irreducible rational curve E ⊂ X ′ 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 = P 2 .
ISSN:0009-725X
1973-4409
DOI:10.1007/s12215-016-0285-3