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 nearO, in t...

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Detalles Bibliográficos
Autores: Ciliberto, Ciro, Farnik, Michal|||0000-0002-7106-0719, Küronya, Alex, Lozovanu, Victor, Roé Vellvé, Joaquim|||0000-0003-0033-8442, Shramov, Constantin|||0000-0001-6952-0651
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:175899
Acceso en línea:https://ddd.uab.cat/record/175899
https://dx.doi.org/urn:doi:10.1007/s12215-016-0285-3
Access Level:acceso abierto
Palabra clave:Newton-Okounkov body
Valuative tree
Valuation
Linear system
Algebraic geometry
Descripción
Sumario: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 nearO, 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=P2.