On cohomology algebras of complex subspace arrangements

Feichtner, Eva; Ziegler, Günter

doi:10.1090/S0002-9947-00-02537-X

On cohomology algebras of complex subspace arrangements
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by Eva Maria Feichtner and Günter M. Ziegler

Trans. Amer. Math. Soc. 352 (2000), 3523-3555

DOI: https://doi.org/10.1090/S0002-9947-00-02537-X

Published electronically: March 2, 2000

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Abstract:

The integer cohomology algebra of the complement of a complex subspace arrangement with geometric intersection lattice is completely determined by the combinatorial data of the arrangement. We give a combinatorial presentation of the cohomology algebra in the spirit of the Orlik-Solomon result on the cohomology algebras of complex hyperplane arrangements. Our methods are elementary: we work with simplicial models for the complements that are induced by combinatorial stratifications of complex space. We describe simplicial cochains that generate the cohomology. Among them we distinguish a linear basis, study cup product multiplication, and derive an algebra presentation in terms of generators and relations.

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