Variétés polaires locales: quelques résultats. (French) Zbl 0572.14002

This paper expands the author’s previous note [C. R. Acad. Sci., Paris, Sér. A 290, 799–802 (1980; Zbl 0496.32009)]. In particular, relative local polar varieties are defined and two transversality results concerning them are shown. The main result then is the equivalence between (local) constancy of the multiplicities of the polar varieties and fulfillment of the Whitney conditions. For a more detailed treatment of these and related topics the reader should consult the author’s paper “Variétés polaires. II”, in Algebraic geometry, Proc. Int. Conf., La Rábida/Spain 1981, Lect. Notes Math. 961, 314–491 (1982; Zbl 0585.14008)].
Reviewer: Ragni Piene (Oslo)


14B05 Singularities in algebraic geometry
32C35 Analytic sheaves and cohomology groups
13H15 Multiplicity theory and related topics