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A
blowup algebra for hyperplane arrangements
Mehdi Garrousian, Aron Simis and Ştefan O. Tohăneanu |
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Vol. 12 (2018), No. 6, 1401–1429
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Abstract |
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It is shown that the Orlik–Terao algebra is graded isomorphic to the special fiber of the ideal generated by the -fold products of the members of a central arrangement of size . This momentum is carried over to the Rees algebra (blowup) of 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 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
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Mathematical Subject Classification 2010
Primary: 13A30, 14N20
Secondary: 13C14, 13D02, 13D05
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Milestones
Received: 11 February 2017
Revised: 5 March 2018
Accepted: 8 April 2018
Published: 6 October 2018
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Authors |
| Mehdi Garrousian | |
| Departamento de Matemáticas Universidad de los Andes Bogotá Colombia |
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| Aron Simis | |
| Departamento de Matemática Universidade Federal de Pernambuco Recife, Pernambuco Brazil |
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| Ştefan O. Tohăneanu | |
| Department of Mathematics University of Idaho Moscow, ID United States |
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