Finite determinacy of dicritical singularities in

Gabriel Calsamiglia-Mendlewicz[1]

  • [1] Universidade Federal Fluminense Departamento de Matemática Aplicada Rua Mário Santos Braga S/N 24020-140 Niterói Rio de Janeiro (Brasil)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 2, page 673-691
  • ISSN: 0373-0956

Abstract

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For germs of singularities of holomorphic foliations in which are regular after one blowing-up we show that there exists a functional analytic invariant (the transverse structure to the exceptional divisor) and a finite number of numerical parameters that allow us to decide whether two such singularities are analytically equivalent. As a result we prove a formal-analytic rigidity theorem for this kind of singularities.

How to cite

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Calsamiglia-Mendlewicz, Gabriel. "Finite determinacy of dicritical singularities in $(\mathbb{C}^2,0)$." Annales de l’institut Fourier 57.2 (2007): 673-691. <http://eudml.org/doc/10235>.

@article{Calsamiglia2007,
abstract = {For germs of singularities of holomorphic foliations in $(\mathbb\{C\}^2,0)$ which are regular after one blowing-up we show that there exists a functional analytic invariant (the transverse structure to the exceptional divisor) and a finite number of numerical parameters that allow us to decide whether two such singularities are analytically equivalent. As a result we prove a formal-analytic rigidity theorem for this kind of singularities.},
affiliation = {Universidade Federal Fluminense Departamento de Matemática Aplicada Rua Mário Santos Braga S/N 24020-140 Niterói Rio de Janeiro (Brasil)},
author = {Calsamiglia-Mendlewicz, Gabriel},
journal = {Annales de l’institut Fourier},
keywords = {Dicritical singularities; holomorphic singular foliations; foliations; dicritical singularities, topological classification of germs of foliations; analytic invariants of germs of foliations; finite determinacy of germs of foliations},
language = {eng},
number = {2},
pages = {673-691},
publisher = {Association des Annales de l’institut Fourier},
title = {Finite determinacy of dicritical singularities in $(\mathbb\{C\}^2,0)$},
url = {http://eudml.org/doc/10235},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Calsamiglia-Mendlewicz, Gabriel
TI - Finite determinacy of dicritical singularities in $(\mathbb{C}^2,0)$
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 2
SP - 673
EP - 691
AB - For germs of singularities of holomorphic foliations in $(\mathbb{C}^2,0)$ which are regular after one blowing-up we show that there exists a functional analytic invariant (the transverse structure to the exceptional divisor) and a finite number of numerical parameters that allow us to decide whether two such singularities are analytically equivalent. As a result we prove a formal-analytic rigidity theorem for this kind of singularities.
LA - eng
KW - Dicritical singularities; holomorphic singular foliations; foliations; dicritical singularities, topological classification of germs of foliations; analytic invariants of germs of foliations; finite determinacy of germs of foliations
UR - http://eudml.org/doc/10235
ER -

References

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