A blowup algebra of hyperplane arrangements
Commutative Algebra
2018-10-17 v1 Algebraic Geometry
Abstract
It is shown that the Orlik-Terao algebra is graded isomorphic to the special fiber of the ideal generated by the -fold products of the members of a central arrangement of size . This momentum is carried over to the Rees algebra (blowup) of and it is shown that this algebra is of fiber-type and Cohen-Macaulay. It follows by a result of Simis-Vasconcelos that the special fiber of is Cohen-Macaulay, thus giving another proof of a result of Proudfoot-Speyer about the Cohen-Macauleyness of the Orlik-Terao algebra.
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Cite
@article{arxiv.1701.03470,
title = {A blowup algebra of hyperplane arrangements},
author = {Mehdi Garrousian and Aron Simis and Stefan Tohaneanu},
journal= {arXiv preprint arXiv:1701.03470},
year = {2018}
}
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22 pages