Équisingularité réelle II : invariants locaux et conditions de régularité

Comte, Georges; Merle, Michel

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 41 (2008) no. 2, pp. 221-269.

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.

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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