Holešová, Michaela Some monomial curves as set-theoretic complete intersections. (English) Zbl 1114.14303 Acta Math. Univ. Ostrav. 12, No. 1, 33-39 (2004). Summary: We describe associated prime ideals of some monomial curves in \(\mathbb{A}^4\). We use a procedure by which we prove that these curves are the intersection of three hypersurfaces and we find their concrete description. MSC: 14R05 Classification of affine varieties 14M10 Complete intersections 14Q05 Computational aspects of algebraic curves × Cite Format Result Cite Review PDF Full Text: EuDML References: [1] H. Bresinsky: Binomial generating sets for monomial curves, with applications in A4. Rend. Sem. Mat., Univers. Politecn. Torino, 46, 1988, pp. 353-370. · Zbl 0738.14017 [2] H. Bresinsky: Monomial Gorenstein curves in A4 as set-theoretic complete intersections. Manuscripta Math, 27, 1979, pp. 353-358. · Zbl 0407.14022 · doi:10.1007/BF01507291 [3] H. Bresinsky: Symmetric semigroup of integers generated by 4 elements. Manuscripta Math, 17, 1975, pp. 205-219. · Zbl 0317.10061 · doi:10.1007/BF01170309 [4] D. Cox J. Little D. O’Shea: Using Algebraic Geometry. Graduate Texts in Mathematics, Volume 185, Springer-Verlag, 1998. · Zbl 0920.13026 [5] W. Gastinger: Über die Verschwindungsideale monomialer Kurven. Dissertation zur Erlangung des Doktorgrades der Naturwissenschaften, Landshut, 1989. · Zbl 0704.14001 [6] E. Kunz: Einführung in die kommutative Algebra und algebraische Geometric. Vieweg, Braunschweig, 1980. · Zbl 0432.13001 [7] S. Solčan: Monomiálne krivky \(C(p^2, p^2 +p, p^2 +p+1, (p + 1)^2)\) ako množinové úplné prieniky. Zbornik vedeckých prác z medzinárodnej vedeckej konferencie Matematika vo výučbe, výskume a praxi, Nitra 2002, pp. 94 - 97. [8] M. Turčanová: Niektoré monomiálne křivky v \(A^4\) ako množinový úplný prienik. Rigorózna práca, FMFI UK Bratislava, 2000. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.