Families of differential forms on complex spaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 1, p. 119-150
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 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.
Classification:  32C15,  32S35
@article{ASNSP_2003_5_2_1_119_0,
     author = {Ancona, Vincenzo and Gaveau, Bernard},
     title = {Families of differential forms on complex spaces},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 2},
     number = {1},
     year = {2003},
     pages = {119-150},
     zbl = {1170.35358},
     mrnumber = {1990976},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2003_5_2_1_119_0}
}
Ancona, Vincenzo; Gaveau, Bernard. Families of differential forms on complex spaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 1, pp. 119-150. http://www.numdam.org/item/ASNSP_2003_5_2_1_119_0/

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