Toric ideals which are determinantal

Rashid Zaare-Nahandi; Reza Abdolmaleki

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Toric ideals which are determinantal

Commutative Algebra · Submitted 7 Jun 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Given any equigenerated monomial ideal $I$ with the property that the defining ideal $J$ of the fiber cone $ F(I)$ of $I$ is generated by quadratic binomials, we introduce a matrix such that the set of its binomial $2$-minors is a generating set of $J$.

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Given any equigenerated monomial ideal $I$ with the property that the defining ideal $J$ of the fiber cone $ F(I)$ of $I$ is generated by quadratic binomials, we introduce a matrix such that the set of its binomial $2$-minors is a generating set of $J$. In this way, we characterize the fiber cone of sortable and Freiman ideals.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Given any equigenerated monomial ideal $I$ with the property that the defining ideal $J$ of the fiber cone $ F(I)$ of $I$ is generated by quadratic binomials, we introduce a matrix such that the set of its binomial $2$-minors is a generating set of $J$.	contribution 0.91	0.92	0.57	asserted 1.00
s1	In this way, we characterize the fiber cone of sortable and Freiman ideals.	result 0.67	0.89	0.32	asserted 1.00

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Original abstract

Given any equigenerated monomial ideal $I$ with the property that the defining ideal $J$ of the fiber cone $ F(I)$ of $I$ is generated by quadratic binomials, we introduce a matrix such that the set of its binomial $2$-minors is a generating set of $J$. In this way, we characterize the fiber cone of sortable and Freiman ideals.

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2 arXiv papers cite this in 6 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 1 sentence without a confident label

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Construction [ref] .

The image of the Veronese mapping is a determinantal variety; an elementary proof · The construction and the proof · 0.95

Compares with it 1 paper

Primarily, in a completely different approach compared to [ref] , Pucci [ref] have proved that, given the generators of the defining ideal of the Veronese variety, the rank-1 determinantal ideal of certain catalecticant matrix provides the same generators.

The image of the Veronese mapping is a determinantal variety; an elementary proof · Introduction · 0.89

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Acknowledgements The author would like to thank his brother Rashid Zaare-Nahandi for bringing attention to his joint paper [ref] which motivated this note.

The image of the Veronese mapping is a determinantal variety; an elementary proof · The construction and the proof · 0.97

Cites it as background 1 paper

One can find further results in [ref] .

Defining ideals of Cohen-Macaulay fiber cones · Introduction · 0.97

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