On the strongly robust property of toric ideals

Kosta, Dimitra; Thoma, Apostolos; Vlădoiu, Marius

doi:10.1016/j.jalgebra.2022.11.002

Journal of Algebra

2023

DOI: 10.1016/j.jalgebra.2022.11.002

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On the strongly robust property of toric ideals

Dimitra Kosta

Apostolos Thoma²,

Marius Vlădoiu³

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2024

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Cited by 3 publications

References 30 publications

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The strongly robust simplicial complex of monomial curves

Kosta,

Thoma,

Vladoiu

2024

J Algebr Comb

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To every simple toric ideal $$I_T$$ I T one can associate the strongly robust simplicial complex $$\Delta _T$$ Δ T , which determines the strongly robust property for all ideals that have $$I_T$$ I T as their bouquet ideal. We show that for the simple toric ideals of monomial curves in $$\mathbb {A}^{s}$$ A s , the strongly robust simplicial complex $$\Delta _T$$ Δ T is either $$\{\emptyset \}$$ { ∅ } or contains exactly one 0-dimensional face. In the case of monomial curves in $$\mathbb {A}^{3}$$ A 3 , the strongly robust simplicial complex $$\Delta _T$$ Δ T contains one 0-dimensional face if and only if the toric ideal $$I_T$$ I T is a complete intersection ideal with exactly two Betti degrees. Finally, we provide a construction to produce infinitely many strongly robust ideals with bouquet ideal the ideal of a monomial curve and show that they are all produced this way.

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The strongly robust simplicial complex of monomial curves

Kosta,

Thoma,

Vladoiu

2024

J Algebr Comb

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Self-dual projective toric varieties and their ideals

Thoma,

Vladoiu

2024

Collect. Math.

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Asymptotic behavior of Markov complexity

Onn,

Thoma,

Vladoiu

2024

Journal of Pure and Applied Algebra

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On the strongly robust property of toric ideals

Cited by 3 publications

References 30 publications

The strongly robust simplicial complex of monomial curves

The strongly robust simplicial complex of monomial curves

Self-dual projective toric varieties and their ideals

Asymptotic behavior of Markov complexity

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