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
Milestones
Received: 11 February 2017
Revised: 5 March 2018
Accepted: 8 April 2018
Published: 6 October 2018
Authors
 Mehdi Garrousian Departamento de Matemáticas Universidad de los Andes Bogotá Colombia Aron Simis Departamento de Matemática Universidade Federal de Pernambuco Recife, Pernambuco Brazil Ştefan O. Tohăneanu Department of Mathematics University of Idaho Moscow, ID United States