an:03912508
Zbl 0572.14002
Teissier, B.
Vari??t??s polaires locales: Quelques resultats
FR
Inst. ??lie Cartan, Univ. Nancy I 3, 33-55 (1981).
00182612
1981
j
14B05 32C35 13H15
Nash modification; Whitney stratification; transversality; multiplicities of the polar varieties; Whitney conditions
This paper expands the author's previous note [C. R. Acad. Sci., Paris, S??r. 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 ''Vari??t??s polaires. II'', in Algebraic Geometry, Proc. internat. Conf., La Rabida/Spain 1981, Lect. Notes Math. 961, 314-491 (1982)].
R.Piene
Zbl 0496.32009