Journal of Commutative Algebra

Cohen-Macaulayness of Rees algebras of diagonal ideals

Kuei-Nuan Lin

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Abstract

Given two determinantal rings over a field $k$, we consider the Rees algebra of the diagonal ideal, the kernel of the multiplication map. The special fiber ring of the diagonal ideal is the homogeneous coordinate ring of the secant variety. When the Rees algebra and the symmetric algebra coincide, we show that the Rees algebra is Cohen-Macaulay.

Article information

Source
J. Commut. Algebra, Volume 6, Number 4 (2014), 561-586.

Dates
First available in Project Euclid: 5 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.jca/1420466344

Digital Object Identifier
doi:10.1216/JCA-2014-6-4-561

Mathematical Reviews number (MathSciNet)
MR3294862

Zentralblatt MATH identifier
1360.13013

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 05E40: Combinatorial aspects of commutative algebra

Keywords
Rees algebra secant variety determinantal ring symmetric algebra Alexander dual regularity Cohen-Macaulay

Citation

Lin, Kuei-Nuan. Cohen-Macaulayness of Rees algebras of diagonal ideals. J. Commut. Algebra 6 (2014), no. 4, 561--586. doi:10.1216/JCA-2014-6-4-561. https://projecteuclid.org/euclid.jca/1420466344


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