Pacific Journal of Mathematics

Equisingularity theory for plane curves with embedded points.

A. Nobile

Article information

Pacific J. Math., Volume 170, Number 2 (1995), 543-566.

First available in Project Euclid: 6 December 2004

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H20: Singularities, local rings [See also 13Hxx, 14B05]
Secondary: 14H45: Special curves and curves of low genus


Nobile, A. Equisingularity theory for plane curves with embedded points. Pacific J. Math. 170 (1995), no. 2, 543--566.

Export citation


  • [2] Let JF',G' be as in (1), then [FGf] -> T is etale if and only if both
  • [A] M. Artin, Algebraic approximation of structures over complete local rings, Pub. Math. Inst. Hautes Etudes Sci., No. 36 (1969), 23-58.
  • [BG] C. Briicker andG.M. Greuel, Deformationen isolierter Kurvensingularitatenmit eingebettenKomponenten, Manuscripta Math, 70 (1990), 93-114.
  • [Br] J. Briancon, Description deHilbnC{x, y}, Invent. Math., 41 (1977), 45-89.
  • [Bu] L. Burch, On Ideals of finite homologicaldimension in localrings1 Proc. Camb. Phil. Soc, 64 (1968), 941-948.
  • [C] E. Casas, Moduli of algebroid plane curves, Lecture Notes in Mathematics, 961, Springer, Berlin-N.Y., (1982), 32-83.
  • [EC] F. Enriques and O. Chisini, Teoria geometrica delle equazioni e della funzioni alge- briche, Vol 2, Zanichelli, Bologna (1918).
  • [F] G. Fischer, Complex analytic geometry, Lecture Notes in Math 538, Springer, Berlin-N.Y., (1976).
  • [H] R. Hartshorne, Algebraic Geometry, Springer, N.Y., (1977).
  • [HI] M. Hermann, S. Ikeda and U. Orbanz, Equimultiplicity and blowing-up, Springer, Berlin (1988).
  • [LI] J. Lipman, Equimultiplicity, reduction and blowing-up, in Commutative Algebra- Analytic methods, ed R.N. Draper, Lect. notes in Pure and Ap. Math, Vol. 68, M. Dekker (1982) (111-147).
  • [L2] J. Lipman, On completeidealsin regularlocal rings,in Alg. Geometry and Commu- tative Algebra (in honor of M. Nagata), Academic Press, San Diego (1987) 203-231.
  • [P] F. Pham. Deformations equisingulieresdes ideaux jacobiens de courbesplanes, in Lecture Notes in Math. 209, Springer, Berlin (1971), 218-233.
  • [R] J-J. Risler, Sur les deformations equisingulieresd'ideaux, Bull. Soc. Math France, 101 (1973), 3-16.
  • [Tl] B. Teissier, Varietes polaires II, in Lecture Notes in Math. 961, Springer, Berlin- N.Y., (1982), 314-491.
  • [T2] B. Teissier, Cycles eanescentes et resolution simultanee, I, II, in Springer Lecture Notes No. 777 (1980).
  • [Z] O. Zariski, Contributions to the problem of equisingularity, in "Questions on alge- braic varieties" Ed. E. Marchionna, Cremonese, Roma (1970), 261-343.
  • [ZS] O. Zariski and P. Samuel, Commutative algebra, Vol. II, Van Nostrand,Princeton (1960).

See also

  • Corr : A. Nobile. Correction to: ``On equisingular families of isolated singularities''. Pacific Journal of Mathematics volume 91, issue 2, (1980), pp. 489-490.