## Algebra & Number Theory

### The equations defining blowup algebras of height three Gorenstein ideals

#### 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.

#### Article information

Source
Algebra Number Theory, Volume 11, Number 7 (2017), 1489-1525.

Dates
Revised: 17 October 2016
Accepted: 19 December 2016
First available in Project Euclid: 12 December 2017

https://projecteuclid.org/euclid.ant/1513096737

Digital Object Identifier
doi:10.2140/ant.2017.11.1489

Mathematical Reviews number (MathSciNet)
MR3697146

Zentralblatt MATH identifier
06775551

#### Citation

Kustin, Andrew; Polini, Claudia; Ulrich, Bernd. The equations defining blowup algebras of height three Gorenstein ideals. Algebra Number Theory 11 (2017), no. 7, 1489--1525. doi:10.2140/ant.2017.11.1489. https://projecteuclid.org/euclid.ant/1513096737

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