Families of differential forms on complex spaces

Vincenzo Ancona; Bernard Gaveau

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2003)

  • Volume: 2, Issue: 1, page 119-150
  • ISSN: 0391-173X

Abstract

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On every reduced complex space X we construct a family of complexes of soft sheaves Λ X ; each of them is a resolution of the constant sheaf ℂ X and induces the ordinary De Rham complex of differential forms on a dense open analytic subset of X . The construction is functorial (in a suitable sense). Moreover each of the above complexes can fully describe the mixed Hodge structure of Deligne on a compact algebraic variety.

How to cite

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Ancona, Vincenzo, and Gaveau, Bernard. "Families of differential forms on complex spaces." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 2.1 (2003): 119-150. <http://eudml.org/doc/84493>.

@article{Ancona2003,
abstract = {On every reduced complex space $X$ we construct a family of complexes of soft sheaves $\Lambda _X$; each of them is a resolution of the constant sheaf $\mathbb \{C\}_X$ and induces the ordinary De Rham complex of differential forms on a dense open analytic subset of $X$. The construction is functorial (in a suitable sense). Moreover each of the above complexes can fully describe the mixed Hodge structure of Deligne on a compact algebraic variety.},
author = {Ancona, Vincenzo, Gaveau, Bernard},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {1},
pages = {119-150},
publisher = {Scuola normale superiore},
title = {Families of differential forms on complex spaces},
url = {http://eudml.org/doc/84493},
volume = {2},
year = {2003},
}

TY - JOUR
AU - Ancona, Vincenzo
AU - Gaveau, Bernard
TI - Families of differential forms on complex spaces
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2003
PB - Scuola normale superiore
VL - 2
IS - 1
SP - 119
EP - 150
AB - On every reduced complex space $X$ we construct a family of complexes of soft sheaves $\Lambda _X$; each of them is a resolution of the constant sheaf $\mathbb {C}_X$ and induces the ordinary De Rham complex of differential forms on a dense open analytic subset of $X$. The construction is functorial (in a suitable sense). Moreover each of the above complexes can fully describe the mixed Hodge structure of Deligne on a compact algebraic variety.
LA - eng
UR - http://eudml.org/doc/84493
ER -

References

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  5. [AG4] V. Ancona – B. Gaveau, The De Rham complex of a reduced complex space, In: “Contribution to complex analysis and analytic geometry”, H. Skoda and J. M. Trépreau (eds.), Vieweg, 1994. Zbl0827.32005MR1319343
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  15. [GNPP2] F. Guillèn – V. Navarro Aznar – P. Pascual Gainza – P. Puertas, Hyperrésolutions cubiques et descente cohomologique, Lecture notes in Math. 1335, Springer, 1988. Zbl0638.00011
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