Skip to main content
SpringerLink
Log in

Deformations and the milnor number of non-isolated plane curve singularities

  • Conference paper
  • First Online:
Singularity Theory and its Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1462))

Abstract

We consider deformations of non-isolated plane curve singularities and compute the number of special points occuring in such a deformation. These numerical data are used to give formulae for the Milnor number of the non-isolated singularity.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. N. A'Campo, Le groupe de monodromie du déploiement des singularités isolées de courbes planes I, Math. Annalen, 213 (1975), pp. 1–32.

    Article  MATH  MathSciNet  Google Scholar 

  2. V.I. Arnol'd, S.M. Gusein-Sade, A.N. Varchenko: Singularities of Differentiable Maps II, Birkhäuser, 1988

    Google Scholar 

  3. R.-O. Buchweitz and G.-M. Greuel: The Milnor Number and Deformations of Complex Curve Singularities, Invent. Math., 58 (1980), pp. 241–281

    Article  MATH  MathSciNet  Google Scholar 

  4. W. Ebeling: The Monodromy Groups of Isolated Singularities of Complete Intersections, Springer LNM 1293, 1987

    Google Scholar 

  5. D. Eisenbud and W.D. Neumann: Three-Dimensional Link Theory and Invariants of Plane Curve Singularities, Annals of Mathematics Study 110, Princeton U.P., 1985

    Google Scholar 

  6. Th.de Jong: Some Classes of Line Singularities: Math. Zeit. 198 (1988), pp. 493–517

    Article  MATH  Google Scholar 

  7. Lê D.T., F. Michel and C. Weber: Courbes polaires et topologie des courbes planes, preprint Genève 1988

    Google Scholar 

  8. R. Pellikaan: Hypersurface Singularities and Resolutions of Jacobi Modules, Thesis, Utrecht 1985

    Google Scholar 

  9. R. Pellikaan: Finite Determinacy of Functions with Non-Isolated Singularities, Proc. London Math. Soc. (3) 57 (1988) pp. 357–382

    Article  MATH  MathSciNet  Google Scholar 

  10. R. Pellikaan: Deformations of Hypersurfaces with a One-Dimensional Singular Locus, preprint Vrije Universiteit Amsterdam 1987, to appear in Journal of Pure and Applied Algebra

    Google Scholar 

  11. R. Schrauwen: Topological Series of Isolated Plane Curve Singularities, preprint Utrecht January 1989, to appear in L'Enseignement Mathématique

    Google Scholar 

  12. D. Siersma: Isolated Line Singularities Proc. Symp. Pure Maths 40 (1983) Part 2, pp. 485–496

    Article  MathSciNet  Google Scholar 

  13. D. Siersma: Singularities with Critical Locus a One-Dimensional Complete Intersection and Transversal Type A 1, Topology and its Applications 27 (1987), pp. 51–73.

    Article  MATH  MathSciNet  Google Scholar 

  14. D. Siersma: Hypersurfaces with Singular Locus a Plane Curve and Transversal Type A 1, Proc. Warsaw Semester on Singularities, Banach Center Publ. 20, PWN-Polish Scientific Publ., Warsaw 1988, pp. 397–410

    Google Scholar 

  15. D. Siersma: Variation Mappings on 1-Isolated Singularities, Preprint Utrecht, to appear in Topology.

    Google Scholar 

  16. E.H. Spanier: Algebraic Topology, New York etc., McGraw-Hill, 1966

    MATH  Google Scholar 

  17. Th. Schulze-Röbbecke: Algorithmen zur Auflösung und Deformation von Singularitäten ebener Kurven, Bonner Math. Schrift Nr. 96, Bonn 1977

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisch Instituut, Rijksuniversiteit Utrecht, P.O. Box 80010, 3508 TA, Utrecht, The Netherlands

    Rob Schrauwen

Authors
  1. Rob Schrauwen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

David Mond James Montaldi

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Schrauwen, R. (1991). Deformations and the milnor number of non-isolated plane curve singularities. In: Mond, D., Montaldi, J. (eds) Singularity Theory and its Applications. Lecture Notes in Mathematics, vol 1462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086388

Download citation

  • DOI: https://doi.org/10.1007/BFb0086388

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53737-3

  • Online ISBN: 978-3-540-47060-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation