Toric embedded resolutions of quasi-ordinary hypersurface singularities

Pedro D. González Pérez[1]

  • [1] Université Paris VII, Institut de Mathématiques, UMR CNRS 7586, Équipe Géométrie et et Dynamique, Case 7012, 2 place Jussieu, 75251 Paris Cedex 05 (France)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 6, page 1819-1881
  • ISSN: 0373-0956

Abstract

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We build two embedded resolution procedures of a quasi-ordinary singularity of complex analytic hypersurface, by using toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection of the singularity. This result answers an open problem of Lipman in Equisingularity and simultaneous resolution of singularities, Resolution of Singularities, Progress in Mathematics No. 181, 2000, 485- 503. In the first procedure the singularity is embedded as hypersurface. In the second procedure, which is inspired by a work of Goldin and Teissier for plane curves (see Resolving singularities of plane analytic branches with one toric morphism, loc. cit., pages 315-340), we re-embed the singularity in an affine space of bigger dimension in such a way that one toric morphism provides its embedded resolution. We compare both procedures and we show that they coincide under suitable hypothesis.

How to cite

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González Pérez, Pedro D.. "Toric embedded resolutions of quasi-ordinary hypersurface singularities." Annales de l’institut Fourier 53.6 (2003): 1819-1881. <http://eudml.org/doc/116086>.

@article{GonzálezPérez2003,
abstract = {We build two embedded resolution procedures of a quasi-ordinary singularity of complex analytic hypersurface, by using toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection of the singularity. This result answers an open problem of Lipman in Equisingularity and simultaneous resolution of singularities, Resolution of Singularities, Progress in Mathematics No. 181, 2000, 485- 503. In the first procedure the singularity is embedded as hypersurface. In the second procedure, which is inspired by a work of Goldin and Teissier for plane curves (see Resolving singularities of plane analytic branches with one toric morphism, loc. cit., pages 315-340), we re-embed the singularity in an affine space of bigger dimension in such a way that one toric morphism provides its embedded resolution. We compare both procedures and we show that they coincide under suitable hypothesis.},
affiliation = {Université Paris VII, Institut de Mathématiques, UMR CNRS 7586, Équipe Géométrie et et Dynamique, Case 7012, 2 place Jussieu, 75251 Paris Cedex 05 (France)},
author = {González Pérez, Pedro D.},
journal = {Annales de l’institut Fourier},
keywords = {singularities; embedded resolution; discriminant; topological type; embedded reolution},
language = {eng},
number = {6},
pages = {1819-1881},
publisher = {Association des Annales de l'Institut Fourier},
title = {Toric embedded resolutions of quasi-ordinary hypersurface singularities},
url = {http://eudml.org/doc/116086},
volume = {53},
year = {2003},
}

TY - JOUR
AU - González Pérez, Pedro D.
TI - Toric embedded resolutions of quasi-ordinary hypersurface singularities
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 6
SP - 1819
EP - 1881
AB - We build two embedded resolution procedures of a quasi-ordinary singularity of complex analytic hypersurface, by using toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection of the singularity. This result answers an open problem of Lipman in Equisingularity and simultaneous resolution of singularities, Resolution of Singularities, Progress in Mathematics No. 181, 2000, 485- 503. In the first procedure the singularity is embedded as hypersurface. In the second procedure, which is inspired by a work of Goldin and Teissier for plane curves (see Resolving singularities of plane analytic branches with one toric morphism, loc. cit., pages 315-340), we re-embed the singularity in an affine space of bigger dimension in such a way that one toric morphism provides its embedded resolution. We compare both procedures and we show that they coincide under suitable hypothesis.
LA - eng
KW - singularities; embedded resolution; discriminant; topological type; embedded reolution
UR - http://eudml.org/doc/116086
ER -

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