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 multi-homogeneous structures. Our main tool is a rigidity statement for radical Borel-fixed ideals in multigraded polynomial rings. For a more detailed exposition of the matter of this chapter we refer to the paper “Universal Gröbner bases for maximal minors” arXiv:1302.4461 written with Emanuela De Negri and Elisa Gorla.
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Conca, A. (2015). Universal Gröbner Bases for Maximal Minors of Matrices of Linear Forms. In: Benedetti, B., Delucchi, E., Moci, L. (eds) Combinatorial Methods in Topology and Algebra. Springer INdAM Series, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-20155-9_6
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DOI: https://doi.org/10.1007/978-3-319-20155-9_6
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