Journal of Commutative Algebra

Cohen-Macaulayness of Rees algebras of diagonal ideals

Kuei-Nuan Lin

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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.

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

First available in Project Euclid: 5 January 2015

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Zentralblatt MATH identifier

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

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


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.

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