Skip to main content

Differential forms and hypersurface singularities

  • 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.

References

  1. Arnold, V.I.: Normal forms of Poisson structures and of other powers of volume forms, Tr. Sem. I.G. Petrovskogo, 12, 1–15 (1985).

    Google Scholar 

  2. Arnold, V.I., Gusein-Zade, S.M., Varchenko, A.N.: Singularities of Differentiable Maps, vol. I, Monographs in Math. 82, Birkhäuser 1985.

    Google Scholar 

  3. Briançon, J., Skoda, H.: Sur la cloture intégrale d'un idéale de germes de fonctions holomorphes en un point de ℂn, C.R. Acad. Sci. Paris 278, 949–951 (1974).

    MATH  Google Scholar 

  4. Brieskorn, E.: Die Monodromie der isolierten Singularitäten von Hyperflächen, Manuscripta math. 2, 103–161 (1970).

    Article  MATH  MathSciNet  Google Scholar 

  5. Brieskorn, E., Knörrer, H.: Plane Algebraic Curves, Birkhäuser 1986.

    Google Scholar 

  6. Deligne, P.: Theorie de Hodge II, III, Publ. Math. IHES 40, 5–58 (1971) and 44, 5–77 (1974).

    MATH  MathSciNet  Google Scholar 

  7. Deligne, P., Dimca, A.: Filtrations de Hodge et par l'ordre du pôle pour les hypersurfaces singulières Ann. Sci. Ec. Norm. Sup. (to appear).

    Google Scholar 

  8. Dimca, A.: On analytic abelian coverings, Math. Ann. 279, 501–515 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  9. Dimca, A.: On the Milnor fibrations of weighted homogeneous polynomials, Compositio Math. (to appear).

    Google Scholar 

  10. Dimca, A.: Betti numbers of hypersurfaces and defects of linear systems, Duke Math. J. 60, 285–298 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  11. Dimca, A.: On the de Rham cohomology of a hypersurface complement, Amer. J. Math. (to appear).

    Google Scholar 

  12. Durfee, A.H.: Mixed Hodge structures on punctured neighborhoods, Duke Math. J. 50, 1017–1040 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  13. Greuel, G.-M.: Der Gauss-Manin-Zusammenhang isolierter Singularitäten von vollständigen Durchschnitten, Math. Ann. 214, 235–266 (1975).

    Article  MATH  MathSciNet  Google Scholar 

  14. Grothendieck, A.: On the de Rham cohomology of algebraic varieties, Publ. Math. IHES 29, 351–358 (1966).

    MATH  Google Scholar 

  15. Karpishpan, Y.: Pole order filtration on the cohomology of algebraic links (preprint MIT).

    Google Scholar 

  16. Kouchnirenko, A.G.: Polyèdres de Newton et nombres de Milnor, Invent. Math. 32, 1–31 (1976).

    Article  MathSciNet  Google Scholar 

  17. Looijenga, E.J.N.: Isolated Singular Points on Complete Intersections, London Math. Soc. Lecture Note Series 77, Cambridge Univ. Press, 1984.

    Google Scholar 

  18. Malgrange, B.: Intégrales asymptotiques et monodromie, Ann. Sci. Ecole Norm. Sup. 7, 405–430 (1974).

    MATH  MathSciNet  Google Scholar 

  19. Milnor, J.: Singular Points of Complex Hypersurfaces. Ann. of Math. Studies 61, Princeton Univ. Press, 1968.

    Google Scholar 

  20. Orlik. P., Solomon, P., Solomon, L.: Singularities I, Hypersurfaces with an isolated singularity, Adv. in Math. 27, 256–272 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  21. Saito, K.: Quasihomogene isolierte Singularitäten von Hyperflächen, Invent. Math. 14, 123–142 (1971).

    Article  MATH  MathSciNet  Google Scholar 

  22. Scheja, G., Wiebe, H.: Über Derivationen in isolierten Singularitäten auf vollständigen Durchschnitten, Math. Ann. 225, 161–171 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  23. Scherk, J.: Isolated Singular Points and the Gauss-Manin Connection, D. Ph. Thesis, Oxford, 1977.

    Google Scholar 

  24. Scherk, J.: On the monodromy theorem for isolated hypersurface singularities, Invent. Math. 58, 289–301 (1980).

    Article  MATH  MathSciNet  Google Scholar 

  25. Scherk, J., Steenbrink, J.H.M.: On the mixed Hodge structure on the cohomology of the Milnor fiber, Math. Ann. 271, 641–665 (1985).

    Article  MATH  MathSciNet  Google Scholar 

  26. Steenbrink, J.H.M.: Intersection form for quasihomogeneous singularities, Compositio Math. 34, 211–223 (1977).

    MATH  MathSciNet  Google Scholar 

  27. Steenbrink, J.H.M.: Mixed Hodge structure on the vanishing cohomology. In: Holm, P. ed.: Real and Complex Singularities, pp. 525–563, Oslo 1976, Alphen aan de Rijn Sijthoff, Noordhoff 1977.

    Google Scholar 

  28. Steenbrink, J.H.M.: Mixed Hodge structures associated with isolated singularities, Proc. Symp. Pure Math. 40, Part 2, pp. 513–536 (1983).

    Article  MathSciNet  Google Scholar 

  29. Steenbrink, J.H.M.: Mixed Hodge Structures and Singularities (book to appear).

    Google Scholar 

  30. Varchenko, A.N.: Asymptotic Hodge structure in the vanishing cohomology, Math. USSR Izv. 18, 469–512 (1982).

    Article  MATH  Google Scholar 

  31. Varchenko, A.N.: Local classification of volume forms in the presence of a hypersurface, Funct. Anal. Appl. 19 (4), 269–276 (1985).

    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

Dimca, A. (1991). Differential forms and hypersurface 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/BFb0086378

Download citation

  • DOI: https://doi.org/10.1007/BFb0086378

  • 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