A blowup algebra for hyperplane arrangements

Garrousian, Mehdi; Simis, Aron; Tohăneanu, Ştefan

doi:10.2140/ant.2018.12.1401

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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

DOI: 10.2140/ant.2018.12.1401

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 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

Vol. 12, No. 6, 2018