## Journal of Commutative Algebra

- J. Commut. Algebra
- Volume 5, Number 3 (2013), 359-398.

### Rees algebras of diagonal ideals

#### Abstract

There is a natural epimorphism from the symmetric algebra to the Rees algebra of an ideal. When this epimorphism is an isomorphism, we say that the ideal is of linear type. Given two determinantal rings over a field, we consider the diagonal ideal, kernel of the multiplication map. We prove in many cases that the diagonal ideal is of linear type and recover the defining ideal of the Rees algebra. In our cases, the special fiber rings of the diagonal ideals are the homogeneous coordinate rings of the join varieties.

#### Article information

**Source**

J. Commut. Algebra, Volume 5, Number 3 (2013), 359-398.

**Dates**

First available in Project Euclid: 13 January 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.jca/1389621376

**Digital Object Identifier**

doi:10.1216/JCA-2013-5-3-359

**Mathematical Reviews number (MathSciNet)**

MR3161739

**Zentralblatt MATH identifier**

1286.13010

**Subjects**

Primary: 13C40: Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12] 14M12: Determinantal varieties [See also 13C40]

Secondary: 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 14Q15: Higher-dimensional varieties

**Keywords**

Rees algebra join variety determinantal ring Gröbner basis symmetric algebra

#### Citation

Lin, Kuei-Nuan. Rees algebras of diagonal ideals. J. Commut. Algebra 5 (2013), no. 3, 359--398. doi:10.1216/JCA-2013-5-3-359. https://projecteuclid.org/euclid.jca/1389621376