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Quadratic Gr\"obner bases of block diagonal matching field ideals and toric degenerations of Grassmannians

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arxiv 2010.07104 v2 pith:H65LLCHU submitted 2020-10-14 math.AC math.CO

Akihiro Higashitani , Hidefumi Ohsugi This is my paper · ORCID
classification math.ACmath.CO
keywords toricbasesblockdegenerationsdiagonalgrassmanniansidealsmatching
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abstract

In the present paper, we prove that the toric ideals of certain $s$-block diagonal matching fields have quadratic Gr\"obner bases. Thus, in particular, those are quadratically generated. By using this result, we provide a new family of toric degenerations of Grassmannians.

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