Minimal Systems of Binomial Generators for the Ideals of Certain Monomial Curves

Manuel B. Branco, Isabel Colaço and Ignacio Ojeda
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Manuel B. Branco: Departamento de Matemáticas, Universidade de Évora, 7000-671 Evora, Portugal
Isabel Colaço: Departamento de Matemática e Ciências Físicas, Instituto Politécnico de Beja, 7800-295 Beja, Portugal
Ignacio Ojeda: Departamento de Matemáticas, Universidad de Extremadura, 06071 Badajoz, Spain

Mathematics, 2021, vol. 9, issue 24, 1-11

Abstract: Let a , b and n > 1 be three positive integers such that a and ∑ j = 0 n − 1 b j are relatively prime. In this paper, we prove that the toric ideal I associated to the submonoid of N generated by { ∑ j = 0 n − 1 b j } ∪ { ∑ j = 0 n − 1 b j + a ∑ j = 0 i − 2 b j ∣ i = 2 , … , n } is determinantal. Moreover, we prove that for n > 3 , the ideal I has a unique minimal system of generators if and only if a < b − 1 .

Keywords: binomial ideal; semigroup ideal; minimal system of generators; determinantal ideal; Gröbner basis; indispensability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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