Titre :

The valuative tree is the projective limit of Eggers-Wall trees

Auteur(s) :

García Barroso, Evelia Rosa [Auteur]
Universidad de La Laguna [Tenerife - SP] [ULL]
González Pérez, Pedro Daniel [Auteur]
Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] [UCM]
Popescu-Pampu, Patrick [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Titre de la revue :

RACSAM. Real Academia de Ciencias. Serie A, Matemáticas - Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas

Pagination :

4051-4105

Éditeur :

Springer

Date de publication :

2019-03-08

ISSN :

1578-7303

Mot(s)-clé(s) en anglais :

Branch
Characteristic exponent
Contact
Eggers-Wall tree
Newton-Puiseux series
Plane curve singularities
Semivaluation
Splice diagram
Rooted tree
Valuation
Valuative tree

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

Consider a germ C of reduced curve on a smooth germ S of complex analytic surface. Assume that C contains a smooth branch L. Using the Newton-Puiseux series of C relative to any coordinate system (x, y) on S such that L ...
Lire la suite >Consider a germ C of reduced curve on a smooth germ S of complex analytic surface. Assume that C contains a smooth branch L. Using the Newton-Puiseux series of C relative to any coordinate system (x, y) on S such that L is the y-axis, one may define the Eggers-Wall tree Θ_L(C) of C relative to L. Its ends are labeled by the branches of C and it is endowed with three natural functions measuring the characteristic exponents of the previous Newton-Puiseux series, their denominators and contact orders. The main objective of this paper is to embed canonically Θ_L(C) into Favre and Jonsson's valuative tree P(V) of real-valued semivaluations of S up to scalar multiplication, and to show that this embedding identifies the three natural functions on Θ_L(C) as pullbacks of other naturally defined functions on P(V). As a consequence, we prove an inversion theorem generalizing the well-known Abhyankar-Zariski inversion theorem concerning one branch: if L _1 is a second smooth branch of C, then the valuative embeddings of the Eggers-Wall trees Θ _{L _1}( C) and Θ_L(C) identify them canonically, their associated triples of functions being easily expressible in terms of each other. We prove also that the space PpVq is the projective limit of Eggers-Wall trees over all choices of curves C. As a supplementary result, we explain how to pass from Θ_L(C) to an associated splice diagram.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Géométrie Lipschitz des singularités

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T14:40:01Z