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2018 A blowup algebra for hyperplane arrangements
Mehdi Garrousian, Aron Simis, Ştefan O. Tohăneanu
Algebra Number Theory 12(6): 1401-1429 (2018). 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.

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Mehdi Garrousian. Aron Simis. Ştefan O. Tohăneanu. "A blowup algebra for hyperplane arrangements." Algebra Number Theory 12 (6) 1401 - 1429, 2018. https://doi.org/10.2140/ant.2018.12.1401

Information

Received: 11 February 2017; Revised: 5 March 2018; Accepted: 8 April 2018; Published: 2018
First available in Project Euclid: 25 October 2018

zbMATH: 06973915
MathSciNet: MR3864202
Digital Object Identifier: 10.2140/ant.2018.12.1401

Subjects:
Primary: 13A30 , 14N20
Secondary: 13C14 , 13D02 , 13D05

Keywords: Cohen–Macaulay , Orlik–Terao algebra , Rees algebra , special fiber algebra

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.12 • No. 6 • 2018
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