Truncated Local Uniformization of Formal Integrable Differential Forms

  1. Fernández-Duque, M. 1
  2. Cano, F. 1
  1. 1 Universidad de Valladolid
    info

    Universidad de Valladolid

    Valladolid, España

    ROR https://ror.org/01fvbaw18

Revista:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Año de publicación: 2022

Volumen: 21

Número: 1

Tipo: Artículo

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Otras publicaciones en: Qualitative theory of dynamical systems

Resumen

We prove the existence of Local Uniformization for rational codimension one foliations along rational rank one valuations, in any ambient dimension. This result is consequence of the Truncated Local Uniformization of integrable formal differential 1-forms, that we also state and prove in the paper. Thanks to the truncated approach, we perform a classical inductive procedure, based both in the control of the Newton Polygon and in the possibility of avoiding accumulations of values, given by the existence of suitable Tschirnhausen transformations.

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The authors are grateful with O. Piltant, M. Spivakovsky and B. Teissier for many fruitful conversations on the subject. We specially thank the careful referees’ work and helpful comments. This work has been supported by the Spanish Research Project MTM2016-77642-C2-1-P (Grant No. PID2019-105621GB-I00 Spain) and the second author has been supported by the Post-Doctoral Program DGAPA at IM-UNAM (Mexico).

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