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Corpus ID: 119126589

Modular decomposition of the Orlik-Terao algebra of a hyperplane arrangement

@article{Denham2012ModularDO,
title={Modular decomposition of the Orlik-Terao algebra of a hyperplane arrangement},
author={G. Denham and Mehdi Garrousian and Stefan O. Tohaneanu},
journal={arXiv: Commutative Algebra},
year={2012}
}

Let A be a collection of n linear hyperplanes in k^l, where k is an algebraically closed field. The Orlik-Terao algebra of A is the subalgebra R(A) of the rational functions generated by reciprocals of linear forms vanishing on hyperplanes of A. It determines an irreducible subvariety of projective space. We show that a flat X of A is modular if and only if R(A) is a split extension of the Orlik-Terao algebra of the subarrangement A_X. This provides another refinement of Stanley's modular… CONTINUE READING