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 (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.

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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