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arXiv · 1701.03470

A blowup algebra of hyperplane arrangements

Mehdi Garrousian·Aron Simis·Stefan Tohaneanu
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Abstract

It is shown that the Orlik-Terao algebra is graded isomorphic to the special fiber of the ideal $I$ generated by the $(n-1)$-fold products of the members of a central arrangement of size $n$. This momentum is carried over to the Rees algebra (blowup) of $I$ 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 $I$ 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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Mehdi Garrousian, Aron Simis, Stefan Tohaneanu. 2017-01-12. A blowup algebra of hyperplane arrangements. https://doi.org/10.2140/ant.2018.12.1401

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