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arXiv · 2302.14345

Sagbi combinatorics of maximal minors and a Sagbi algorithm

Winfried Bruns·Aldo Conca
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Abstract

The maximal minors of a matrix of indeterminates are a universal Gröbner basis by a theorem of Bernstein, Sturmfels and Zelevinsky. On the other hand it is known that they are not always a universal Sagbi basis. By an experimental approach we discuss their behavior under varying monomial orders and their extensions to Sagbi bases. These experiments motivated a new implementation of the Sagbi algorithm which is organized in a Singular script and falls back on Normaliz for the combinatorial computations. In comparison to packages in the current standard distributions of Macaulay 2 and Singular it extends the range of computability by at least one order of magnitude.

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Winfried Bruns, Aldo Conca. 2023-06-15. Sagbi combinatorics of maximal minors and a Sagbi algorithm. https://arxiv.org/abs/2302.14345

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