{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T22:00:01Z","timestamp":1747173601190,"version":"3.40.5"},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2020,11,16]],"date-time":"2020-11-16T00:00:00Z","timestamp":1605484800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. Aust. Math. Soc."],"published-print":{"date-parts":[[2021,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, we study a family of binomial ideals defining monomial curves in the <jats:italic>n<\/jats:italic>-dimensional affine space determined by <jats:italic>n<\/jats:italic> hypersurfaces of the form \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788720000385_inline1.png\"\/><jats:tex-math>\n$x_i^{c_i} - x_1^{u_{i1}} \\cdots x_n^{u_{1n}}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> in \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788720000385_inline2.png\"\/><jats:tex-math>\n$\\Bbbk [x_1, \\ldots , x_n]$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> with \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788720000385_inline3.png\"\/><jats:tex-math>\n$u_{ii} = 0, \\ i\\in \\{ 1, \\ldots , n\\}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. We prove that the monomial curves in that family are set-theoretic complete intersections. Moreover, if the monomial curve is irreducible, we compute some invariants such as genus, type and Frobenius number of the corresponding numerical semigroup. We also describe a method to produce set-theoretic complete intersection semigroup ideals of arbitrary large height.\n<\/jats:p>","DOI":"10.1017\/s1446788720000385","type":"journal-article","created":{"date-parts":[[2020,11,16]],"date-time":"2020-11-16T07:20:12Z","timestamp":1605511212000},"page":"48-70","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["CRITICAL BINOMIAL IDEALS OF NORTHCOTT TYPE"],"prefix":"10.1017","volume":"110","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2330-9871","authenticated-orcid":false,"given":"P. 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