Mathematische Annalen

, Volume 263, Issue 3, pp 313–321 | Cite as

The bifurcation set and logarithmic vector fields

  • Hiroaki Terao


Vector Field Logarithmic Vector Logarithmic Vector Field 
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  1. 1.
    Arnol'd, V.I.: Indices of singular points of 1-forms on a manifold with boundary, convolution of invariants of reflection groups, and singular projections of smooth surfaces. Usp. Mat. Nauk34, 3–38 (1979); Russian Math. Surveys34, 1–42 (1979)Google Scholar
  2. 2.
    Cartier, P.: Les arrangements d'hyperplans: un chapitre de géometrie combinatoire. Séminaire Bourbaki 33e année, 1980/1981, no 561. Lecture Notes in Mathematics, No. 901. Berlin, Heidelberg, New York: Springer 1982Google Scholar
  3. 3.
    Looijenga, E.: The complement of the bifurcation variety of a simple singularity. Invent. Math.32, 105–116 (1974)Google Scholar
  4. 4.
    Lyashko, O.V.: The geometry of bifurcation diagrams. Usp. Mat. Nauk34, 205–206 (1979); Russian Math. Surveys34, 209–210 (1979)Google Scholar
  5. 5.
    Saito, K.: On the uniformization of complements of discriminant loci. Symp. in Pure Math., Williams College, 1975, Several Complex variables. Providence: AMS 1977Google Scholar
  6. 6.
    Saito, K.: Theory of logarithmic differential forms and logarithmic vector fields. J. Fac. Sci. Univ. Tokyo Sect, IA27, 265–291 (1980)Google Scholar
  7. 7.
    Saito, K.: Primitive forms for an unfolding of a function with an isolated critical point. J. Fac. Sci. Univ. Tokyo Sect. IA28, 775–792 (1982)Google Scholar
  8. 8.
    Teissier, B.: The hunting of invariants in the geometry of discriminants. Real and complex singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976), pp. 565–678. Alphen aan den Rijn: Sijthoff and Noordhoff 1977Google Scholar
  9. 9.
    Terao, H.: Arrangements of hyperplanes and their freeness. I. J. Fac. Sci. Univ. Tokyo Sect. IA27, 293–312 (1980)Google Scholar
  10. 10.
    Terao, H.: Generalized exponents of a free arrangement of hyperplanes and Shephard-Todd-Brieskorn formula. Invent. Math.63, 159–179 (1981)Google Scholar
  11. 11.
    Terao, H.: Discriminant of a holomorphic map and logarithmic vector fields (to appear in J. Fac. Sci. Univ. Tokyo Sect. IA)Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Hiroaki Terao
    • 1
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA

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