Tokyo Journal of Mathematics

The Non-vanishing Cohomology of Orlik-Solomon Algebras


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The cohomology of the complement of hyperplanes with coefficients in the rank one local system associated to a generic weight vanishes except in the highest dimension. In this paper, we construct matroids or arrangements admitting weights for which the Orlik-Solomon algebra has non-vanishing cohomology, using decomposable relations arising from Latin hypercubes.

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Tokyo J. Math., Volume 30, Number 1 (2007), 223-238.

First available in Project Euclid: 20 July 2007

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Zentralblatt MATH identifier

Primary: 52C35: Arrangements of points, flats, hyperplanes [See also 32S22]
Secondary: 32S22: Relations with arrangements of hyperplanes [See also 52C35] 14F99: None of the above, but in this section


KAWAHARA, Yukihito. The Non-vanishing Cohomology of Orlik-Solomon Algebras. Tokyo J. Math. 30 (2007), no. 1, 223--238. doi:10.3836/tjm/1184963658.

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