#### Vol. 12, No. 6, 2018

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A blowup algebra for hyperplane arrangements

### Mehdi Garrousian, Aron Simis and Ştefan O. Tohăneanu

Vol. 12 (2018), No. 6, 1401–1429
##### Abstract

It is shown that the Orlik–Terao algebra is graded isomorphic to the special fiber of the ideal $I$ generated by the $\left(n-1\right)$-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 and Vasconcelos that the special fiber of $I$ is Cohen–Macaulay, thus giving another proof of a result of Proudfoot and Speyer about the Cohen–Macaulayness of the Orlik–Terao algebra.

##### Keywords
Rees algebra, special fiber algebra, Orlik–Terao algebra, Cohen–Macaulay
##### Mathematical Subject Classification 2010
Primary: 13A30, 14N20
Secondary: 13C14, 13D02, 13D05