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Universal and comprehensive Gröbner bases of the classical determinantal ideal

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Let A =(x ij ), i =1,2,... ,k, j =1,2,... ,l, 1 ≤ k ≤ l, be a matrix of independent variables, G be the set of maximal minors of A, and I = (G) be the classical determinantal ideal. We show that G is a universal Gröbner basis of I. Also, a sufficient condition for G to be a universal comprehensive Gröbner basis is proved. Bibliography: 12 titles.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    M. Kalinin

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  1. M. Kalinin
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Correspondence to M. Kalinin.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 373, 2009, pp. 134–143.

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Kalinin, M. Universal and comprehensive Gröbner bases of the classical determinantal ideal. J Math Sci 168, 385–389 (2010). https://doi.org/10.1007/s10958-010-9990-1

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