Real equisingularity II: local invariants and regularity conditions

Georges Comte; Michel Merle

Annales scientifiques de l'École Normale Supérieure (2008)

  • Volume: 41, Issue: 2, page 221-269
  • ISSN: 0012-9593

Abstract

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For germs of subanalytic sets, we define two finite sequences of new numerical invariants. The first one is obtained by localizing the classical Lipschitz-Killing curvatures, the second one is the real analogue of the vanishing Euler characteristics introduced by M. Kashiwara. We show that each invariant of one sequence is a linear combination of the invariants of the other sequence. We then connect our invariants to the geometry of the discriminants of all dimension. Finally we prove that these invariants are continuous along Verdier strata of a closed subanalytic set.

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Comte, Georges, and Merle, Michel. "Équisingularité réelle II : invariants locaux et conditions de régularité." Annales scientifiques de l'École Normale Supérieure 41.2 (2008): 221-269. <http://eudml.org/doc/272117>.

@article{Comte2008,
abstract = {On définit, pour un germe d’ensemble sous-analytique, deux nouvelles suites finies d’invariants numériques. La première a pour termes les localisations des courbures de Lipschitz-Killing classiques, la seconde est l’équivalent réel des caractéristiques évanescentes complexes introduites par M. Kashiwara. On montre que chaque terme d’une de ces suites est combinaison linéaire des termes de l’autre, puis on relie ces invariants à la géométrie des discriminants des projections du germe sur des plans de toutes les dimensions. Il apparaît alors que ces invariants sont continus le long de strates de Verdier d’une stratification sous-analytique d’un fermé.},
author = {Comte, Georges, Merle, Michel},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {sub-analytic set; Lipschitz-Killing curvatures; polar invariant; Verdier strata; Whitney strata},
language = {fre},
number = {2},
pages = {221-269},
publisher = {Société mathématique de France},
title = {Équisingularité réelle II : invariants locaux et conditions de régularité},
url = {http://eudml.org/doc/272117},
volume = {41},
year = {2008},
}

TY - JOUR
AU - Comte, Georges
AU - Merle, Michel
TI - Équisingularité réelle II : invariants locaux et conditions de régularité
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2008
PB - Société mathématique de France
VL - 41
IS - 2
SP - 221
EP - 269
AB - On définit, pour un germe d’ensemble sous-analytique, deux nouvelles suites finies d’invariants numériques. La première a pour termes les localisations des courbures de Lipschitz-Killing classiques, la seconde est l’équivalent réel des caractéristiques évanescentes complexes introduites par M. Kashiwara. On montre que chaque terme d’une de ces suites est combinaison linéaire des termes de l’autre, puis on relie ces invariants à la géométrie des discriminants des projections du germe sur des plans de toutes les dimensions. Il apparaît alors que ces invariants sont continus le long de strates de Verdier d’une stratification sous-analytique d’un fermé.
LA - fre
KW - sub-analytic set; Lipschitz-Killing curvatures; polar invariant; Verdier strata; Whitney strata
UR - http://eudml.org/doc/272117
ER -

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