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The de Rham Complex of a Reduced Analytic Space

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Contributions to Complex Analysis and Analytic Geometry / Analyse Complexe et Géométrie Analytique

Part of the book series: Aspects of Mathematics ((ASMA,volume E 26))

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Abstract

We construct a de Rham complex on a reduced analytic space of fine sheaves of differential forms which are identical to the usual sheaves of C ∞ forms outside the singularities.

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Bibliography

  1. V. Ancona and B. Gaveau. Differential forms and resolutions on certain analytic spaces I Irreducible exceptional divisor. Bull. Sci. Math., 116: 307–324, 1992.

    MathSciNet  MATH  Google Scholar 

  2. V. Ancona and B. Gaveau. Differential forms and resolutions on certain analytic spaces II Flat resolutions. Canadian J. Math., 44: 728–749, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  3. V. Ancona and B. Gaveau. Formes differentielles et résolutions sur certains espaces analytiques. C. R. Acad. Sci. Paris, 314: 133–138, 1992.

    MathSciNet  MATH  Google Scholar 

  4. V. Ancona and B. Gaveau. Modules plats de differentielles sur certains espaces analytiques. C. R. Acad. Sci. Paris, 314: 223–225, 1992.

    MathSciNet  MATH  Google Scholar 

  5. V. Ancona and B. Gaveau. Differential forms and resolutions on certain analytic spaces III Spectral resolutions. Annali di Mathematica,to appear.

    Google Scholar 

  6. T. Bloom and M. Herrera. De Rham cohomology of an analytic space. Invent. Math., 7: 275–296, 1969.

    Article  MathSciNet  Google Scholar 

  7. I. Fary. Valeurs critiques et algèbres spectrales d’une application. Ann. of Math., 63 (2): 437–490, 1956.

    Article  MathSciNet  MATH  Google Scholar 

  8. I. Fary. Cohomologie des variétés algébriques. Ann. of Math., 65 (2): 21–73, 1957.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Ferrari. Cohomology and holomorphic differential forms on complex analytic spaces. Ann. Scuola Norm. Sup. Pisa, 24 (3): 65–77, 1970.

    MathSciNet  MATH  Google Scholar 

  10. H. Grauert. Ein Theorem der analytische Garbentheorie und die Modulräume komplexer Strukturen. Inst. Hautes Etudes Sci. Publ. Math., (5): 64 pp., 1960.

    Google Scholar 

  11. R. Hartshorne. On the de Rham cohomology of algebraic varieties. Publ. Math. LH.E.S., (45): 5–99, 1975.

    Google Scholar 

  12. J. Leray. L’anneau spectral et l’anneau filtré d’homologie d’un espace localement compact et d’une application continue. J. Math. Pures Appl., 29 (9): 1–139, 1950.

    MathSciNet  MATH  Google Scholar 

  13. H. J. Reiffen. Das Lemma von Poincaré für holomorphe Differentialformen auf komplexen Räumen. Math. Z., 101: 269–284, 1967.

    Article  MathSciNet  MATH  Google Scholar 

  14. H. J. Reiffen and U. Vetter. Pfaffsche Formen auf komplexen Räumen. Math. Ann., 167: 338–350, 1966.

    Article  MathSciNet  MATH  Google Scholar 

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Authors
  1. Vincenzo Ancona
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  2. Bernard Gaveau
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Editors and Affiliations

  1. Département de Mathématiques, Université Paris 6, Tour 45-46, 5ème étage, 4, Place Jussieu, F-75252, Paris Cedex 05, France

    Henri Skoda  & Jean-Marie Trépreau  & 

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© 1994 Springer Fachmedien Wiesbaden

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Ancona, V., Gaveau, B. (1994). The de Rham Complex of a Reduced Analytic Space. In: Skoda, H., Trépreau, JM. (eds) Contributions to Complex Analysis and Analytic Geometry / Analyse Complexe et Géométrie Analytique. Aspects of Mathematics, vol E 26. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14196-9_1

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  • DOI: https://doi.org/10.1007/978-3-663-14196-9_1

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-06633-8

  • Online ISBN: 978-3-663-14196-9

  • eBook Packages: Springer Book Archive

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