Teissier, B. Variétés polaires locales: quelques résultats. (French) Zbl 0572.14002 Inst. Élie Cartan, Univ. Nancy I 3, 33-55 (1981). 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) Cited in 1 ReviewCited in 6 Documents MSC: 14B05 Singularities in algebraic geometry 32C35 Analytic sheaves and cohomology groups 13H15 Multiplicity theory and related topics Keywords:Nash modification; Whitney stratification; transversality; multiplicities of the polar varieties; Whitney conditions Citations:Zbl 0496.32009; Zbl 0585.14008 PDFBibTeX XMLCite \textit{B. Teissier}, Inst. Élie Cartan, Univ. Nancy I 3, 33--55 (1981; Zbl 0572.14002)