## Tokyo Journal of Mathematics

### The Non-vanishing Cohomology of Orlik-Solomon Algebras

Yukihito KAWAHARA

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 20 July 2007

https://projecteuclid.org/euclid.tjm/1184963658

Digital Object Identifier
doi:10.3836/tjm/1184963658

Mathematical Reviews number (MathSciNet)
MR2328065

Zentralblatt MATH identifier
1132.52027

#### Citation

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

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