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)


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.


Differential Form Spectral Sequence Complex Manifold Hodge Structure Exterior Product 
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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

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