On polar invariants of hypersurface singularities

Abstract

The author proves a generalization of the Teissier theorem [B. Teissier, Invent. Math. 40, 267-292 (1977; Zbl 0446.32002)] about expressing the topological determinacy order by the polar invariants. In this generalization the main assumption is that the projective tangent cone of the hypersurface has at most isolated singularities. Some consequences of the theorem are studied in the last section of the paper.