Skip to main content

Vanishing cycles for analytic maps

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

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

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

Access this chapter

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.

Bibliography

  1. R.O. Buchweitz and G.-M. Greuel, The Milnor number and deformations of complex curve singularities, Invent. Math. 58 (1980), 241–281

    Article  MATH  MathSciNet  Google Scholar 

  2. L. Burch, On ideals of finite homological dimension in local rings, Math. Proc. Camb. Phil. Soc. 64 (1968), 941–946

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Damon, -equivalence and the equivalence of sections of images and discriminants, these proceedings

    Google Scholar 

  4. J. Damon and D.Mond, -codimension and the vanishing topology of the discriminant, Preprint, University of Warwick, 1989

    Google Scholar 

  5. T. Gaffney, Properties of finitely determined germs, Ph.D. thesis, Brandeis, 1976

    Google Scholar 

  6. C.G. Gibson, A. A. du Plessis, E. J. N. Looijenga, K. Wirthmuller, Topological stability of smooth mappings, Lecture Notes in Math. 552, Springer Verlag, Berlin, 1977

    Google Scholar 

  7. M. Goresky, R. MacPherson, Stratified Morse theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer Verlag, Berlin, 1988

    Book  Google Scholar 

  8. G.-M. Greuel, Dualitat in der lokalen kohomologie isolierter Singularitäten, Math. Ann. 250 (1980,) 157–173

    MATH  MathSciNet  Google Scholar 

  9. H. Hamm, Lokale topologische Eigenschaften komplexer Räume, Math. Annalen 191 (1971), 235–252.

    Article  MATH  MathSciNet  Google Scholar 

  10. T. de Jong, D. van Straten, Deformations of surface singularities, preprint, University of Kaiserslautern, 1988

    Google Scholar 

  11. T. de Jong, D. van Straten, Disentanglements, these proceedings

    Google Scholar 

  12. Lê D. T., Some remarks on relative monodromy, in Real and complex singularities, Per Holm (ed.), Proceedings of Nordic Summer School Oslo 1976, Sijthoff and Noordhoff, Alphen aan den Rijn, 1977.

    Google Scholar 

  13. Lê D. T., Le concept de singularité isolée de fonction analytique, Advanced Studies in Pure Math. 8 (1986), Complex Analytic Singularities, 215–227

    Google Scholar 

  14. E. J. N. Looijenga and J. H. M. Steenbrink, Milnor numbers and Tjurina numbers of complete intersections, Math. Annalen 271 (1985), 121–124

    Article  MATH  MathSciNet  Google Scholar 

  15. W.L. Marar, The Euler characteristic of the disentanglement of the image of a corank 1 map germ, these proceedings

    Google Scholar 

  16. W. L. Marar, D. Mond, Multiple point schemes for corank 1 maps, J. London Math. Soc. (2) 39 (1989), 553–567

    Article  MATH  MathSciNet  Google Scholar 

  17. J. N. Mather, Stability of C∞ mappings IV: Classification of stable germs by R-algebras, Publ. Math. I. H. E. S. 37 (1969), 223–248

    MATH  MathSciNet  Google Scholar 

  18. H. Matsumura, Commutative ring theory, Cambridge University Press, Cambridge, 1986

    MATH  Google Scholar 

  19. D. Mond, Some remarks on the geometry and classification of germs of maps from surfaces to 3-space, Topology 26, 1987, 361–383

    Article  MATH  MathSciNet  Google Scholar 

  20. G. R. Pellikaan, Hypersurface singularities and resolutions of Jacobi modules, Thesis, Rijksuniversiteit Utrecht, 1985

    Google Scholar 

  21. R. Piene, Ideals associated to a desingularisation, Proc. Summer meeting Copenhagen 1978, Lecture Notes in Math. 732, Springer Verlag, Berlin, 1979, 503–517

    Google Scholar 

  22. D. Siersma, Vanishing cycles and special fibres, these proceedings

    Google Scholar 

  23. C. T. C. Wall, Finite determinacy of smooth map-germs, Bull. London Math. Soc. 13 (1981), 481–539

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

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

Mond, D. (1991). Vanishing cycles for analytic maps. 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/BFb0086385

Download citation

  • DOI: https://doi.org/10.1007/BFb0086385

  • 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