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2017 The equations defining blowup algebras of height three Gorenstein ideals
Andrew Kustin, Claudia Polini, Bernd Ulrich
Algebra Number Theory 11(7): 1489-1525 (2017). DOI: 10.2140/ant.2017.11.1489

Abstract

We find the defining equations of Rees rings of linearly presented height three Gorenstein ideals. To prove our main theorem we use local cohomology techniques to bound the maximum generator degree of the torsion submodule of symmetric powers in order to conclude that the defining equations of the Rees algebra and of the special fiber ring generate the same ideal in the symmetric algebra. We show that the ideal defining the special fiber ring is the unmixed part of the ideal generated by the maximal minors of a matrix of linear forms which is annihilated by a vector of indeterminates, and otherwise has maximal possible height. An important step in the proof is the calculation of the degree of the variety parametrized by the forms generating the height three Gorenstein ideal.

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Andrew Kustin. Claudia Polini. Bernd Ulrich. "The equations defining blowup algebras of height three Gorenstein ideals." Algebra Number Theory 11 (7) 1489 - 1525, 2017. https://doi.org/10.2140/ant.2017.11.1489

Information

Received: 19 June 2015; Revised: 17 October 2016; Accepted: 19 December 2016; Published: 2017
First available in Project Euclid: 12 December 2017

zbMATH: 06775551
MathSciNet: MR3697146
Digital Object Identifier: 10.2140/ant.2017.11.1489

Subjects:
Primary: 13A30
Secondary: 13D02, 13D45, 13H15, 14A10, 14E05

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 7 • 2017
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