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Lin, Kuei-Nuan

Cohen-Macaulayness of Rees algebras of diagonal ideals. (English) Zbl 1360.13013

J. Commut. Algebra 6, No. 4, 561-586 (2014).
Summary: 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.

MSC:

13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
13C40 Linkage, complete intersections and determinantal ideals
14M12 Determinantal varieties
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
14Q15 Computational aspects of higher-dimensional varieties
05E40 Combinatorial aspects of commutative algebra
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)

Keywords:

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

Software:

Macaulay2
Cite Review PDF
Full Text: DOI arXiv Euclid

References:

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