In recent publications, we have defined complexes of differential forms on analytic spaces which are resolutions of the constant sheaf. These complexes were used to prove the existence of a mixed Hodge structure on the cohomology of analytic spaces which possess kählerian hypercoverings, in particular, projective algebraic varieties. We define an exterior product on these forms, which induces the cup product on the cohomology of analytic spaces. The main difficulty is to prove that this exterior product is functorial with respect to morphisms of analytic spaces. This exterior product can be used to prove that the cup product is compatible with the mixed Hodge structure on the cohomology.

Exterior products of forms and the cohomology ring of a complex space / V. ANCONA; GAVEAU B. - In: BULLETIN DES SCIENCES MATHEMATIQUES. - ISSN 0007-4497. - STAMPA. - 130:(2006), pp. 525-552. [10.1016/j.bulsci.2005.10.004]

Exterior products of forms and the cohomology ring of a complex space

ANCONA, VINCENZO;
2006

Abstract

In recent publications, we have defined complexes of differential forms on analytic spaces which are resolutions of the constant sheaf. These complexes were used to prove the existence of a mixed Hodge structure on the cohomology of analytic spaces which possess kählerian hypercoverings, in particular, projective algebraic varieties. We define an exterior product on these forms, which induces the cup product on the cohomology of analytic spaces. The main difficulty is to prove that this exterior product is functorial with respect to morphisms of analytic spaces. This exterior product can be used to prove that the cup product is compatible with the mixed Hodge structure on the cohomology.
2006
130
525
552
V. ANCONA; GAVEAU B
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/217596
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