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On the stratification of the discriminant varieties. (English) Zbl 0686.32009

It is shown that the discriminant variety for the arrangements of type \(A_{\ell},B_{\ell}\) and \(D_{\ell}\) has canonical regular stratifications which are constructed in the standard way. Here the regularity means the b-regularity in the sense of Whitney. It is known that the b-regularity implies the a-regularity in the sense of Mather. For \(A_{\ell +1}\) and \(B_{\ell +1}\), we simply take \({\mathcal S}={\mathcal S}_{\min.}\), which is the minimal stratification. As the stratification \({\mathcal S}\) for \(D_{\ell +1}\), we take the restriction of \({\mathcal S}_{\min.}\) for \(B_{\ell +1}\) to \(D_{\ell +1}\).
Reviewer: S.Ohyanagi

MSC:

32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
32S45 Modifications; resolution of singularities (complex-analytic aspects)
58A35 Stratified sets
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References:

[1] N. BOURBAKI, ”Groupes et Algebres de Lie, Chapitres 4, 5 et 6”, Hermann, Paris, 1968. · Zbl 0186.33001
[2] E. BRIESKORN, Sur les groupes de tresses, in ”Seminaire Bourbaki 1971/72, Lecture Note in Math. 317”, Springer, Berlin/Heidelberg/New York, 1973, pp 21-44. · Zbl 0277.55003
[3] P. DELIGNE, Les immeubles des groupes de tresses generalises, Invent. Math. 1 (1972), 273-302. · Zbl 0238.20034 · doi:10.1007/BF01406236
[4] S. LANG, ”Algebra”, Addison-Wesley, Amsterdam-London-Manila-Singapore-Sy dney-Tokyo, 1965. · Zbl 0193.34701
[5] J. MATHER, Stratifications and Mappings, in ”Dynamical Systems, ” edited b Peixoto, 1973, pp. 195-232. · Zbl 0286.58003
[6] P. ORLIK, Introduction to arrangements, · Zbl 0722.51003
[7] H. WHITNEY, Tangents to analytic variety, Ann. Math. 81 (1964), 496-546 · Zbl 0152.27701 · doi:10.2307/1970400
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