Bernstein, Sturmfels and Zelevinsky proved in 1993 that the maximal minors of a matrix of variables form a universal Gröbner basis. We present a very short proof of this result, along with a broad generalization to matrices with multihomogeneous structures. Our main tool is a rigidity statement for radical Borel-fixed ideals in multigraded polynomial rings.
Universal Gröbner Bases for Maximal Minors of Matrices of Linear Forms
CONCA, ALDO
2015-01-01
Abstract
Bernstein, Sturmfels and Zelevinsky proved in 1993 that the maximal minors of a matrix of variables form a universal Gröbner basis. We present a very short proof of this result, along with a broad generalization to matrices with multihomogeneous structures. Our main tool is a rigidity statement for radical Borel-fixed ideals in multigraded polynomial rings.
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