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...
| Autores: | , , , , , |
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| 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 |
| 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. |
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