Advertisement

Differential Forms, Cycles and Hodge Theory on Complex Analytic Spaces

  • Vincenzo Ancona
  • Bernard Gaveau
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 52)

Abstract

We summarize our theory of differential forms on complex analytic spaces. This theory is functorial with respect to analytic mappings. We define also dual complexes of chains, and the integration of forms on chains. We construct a mixed Hodge theory on compact algebraic varieties using these forms.

Keywords

Differential Form Spectral Sequence Complex Manifold Hodge Structure Exterior Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. AG1.
    V. Ancona and B. GaveauLa théorie des résidus sur un espace analytique complexe in Conference Jean Leray(M. de Gosson and J. Vaillant, eds.), Kärlskrona, 1999.Google Scholar
  2. AG2.
    V. Ancona and B. GaveauFamilies of differential forms on complex spacesAnnali Scuola Norm., Pisa.Google Scholar
  3. AG3.
    V. Ancona and B. Gaveau, Differential forms, integration and Hodge theory on complex analytic spaces, preprint, January 2001.Google Scholar
  4. AG4.
    V. Ancona and B. GaveauThe De Rham complex of a reduced space.In: Contribution to complex analysis and analytic geometry, (H. Skoda and J. Trépreau, eds.), Vieweg, 1994.Google Scholar
  5. AG5.
    V. Ancona and B. GaveauTheorémès de De Rham sur un espace analytiqueRevue Roumaine de Mathématiques pures et appliquées 38 (1993), 579–594.MathSciNetzbMATHGoogle Scholar
  6. B-H.
    T. Bloom and M. HerreraDe Rham cohomology of an analytic spaceInvent. Math. 7 (1969), 275–296.MathSciNetCrossRefGoogle Scholar
  7. D-P.
    P. Dolbeault and J. PolyDifferential forms with subanalytic singularities integral cohomology; residues.In: Proceedings of Symposia in Pure Mathematics Vol. 30, 255–261, Academic Press, New York.Google Scholar
  8. E.
    F. ElzeinMixed Hodge structuresTrans. Am. Math. Soc.275(1983), 71–106.MathSciNetzbMATHCrossRefGoogle Scholar
  9. He.
    M. HerreraIntegration on a semi analytic setBull Soc. Math. France94(1966), 141–180.MathSciNetzbMATHGoogle Scholar
  10. Hi.
    H. HironakaIntroduction to real-analytic sets and real analytic mapsInstitute di Matematica, Università di Pisa, 1973.Google Scholar
  11. GNFP.
    E Guillen, V. Navarro Aznar, P. Pascual Guainza, and P. PuertasHyper-resolutions cubiques et descente cohomologique .In: Lecture Notes in Math. 1335, Springer, 1988.Google Scholar
  12. K-M.
    K. Kodaira and J. MorrowComplex manifoldsHolt Rinehart, 1975.Google Scholar
  13. P.
    J. PolyFormule des résidus et intersections de chaînes sous analytiquesThèse Poitiers, 1974Google Scholar
  14. W.
    A. WeilSur les théorèmes de De RhamComment. Math. Helvetici (1951), 119–145.Google Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Vincenzo Ancona
    • 1
  • Bernard Gaveau
    • 2
  1. 1.Dipartimento di Matematica U. DiniUniversità degli StudiFirenzeItaly
  2. 2.Laboratoire Analyse et Physique MathématiqueParisFrance

Personalised recommendations