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Minimally generating ideals defining certain tangent cones. (English) Zbl 0502.14001


MSC:

14A05 Relevant commutative algebra
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
14H20 Singularities of curves, local rings
13E15 Commutative rings and modules of finite generation or presentation; number of generators
14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
14M07 Low codimension problems in algebraic geometry
14B05 Singularities in algebraic geometry
Full Text: DOI

References:

[1] Geramita, A.; Orecchia, F., On the Cohen-Macaulay Type of \(s\)-Lines in \(A^{n + 1}\), J. Algebra, 70, 116-140 (1981) · Zbl 0464.14007
[2] A. Geramita and C. Small; A. Geramita and C. Small · Zbl 0332.13011
[3] Geyer, W.-D, On the Number of Equations Which are Necessary to Describe an Algebraic Set in \(n\)-space, (Lecture Notes, Escola de Algebra (July 1974), University of Brasilia)
[4] Herzog, J.; Kunz, E., Der Kanonische Modul eines Cohen-Macaulay Rings, (Lecture Notes in Mathematics No. 238 (1971), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York) · Zbl 0231.13009
[5] Hironaka, H., Resolution of singularities of an algebraic variety over a field of characteristic 0, Ann. of Math., 79, 109-326 (1964) · Zbl 0122.38603
[6] Murthy, M. P., Generators for certain ideals in regular rings of dimension three, Comment. Math. Helv., 47, 179-184 (1972) · Zbl 0251.13006
[7] Orecchia, F., Points in generic position and conductors of curves with ordinary singularities, J. London Math. Soc., 24, 85-96 (1981) · Zbl 0492.14017
[8] F. OrecchiaCanad. Math. Bull.; F. OrecchiaCanad. Math. Bull. · Zbl 0491.13016
[9] Orecchia, F., One-dimensional local rings with reduced associated graded rings and their Hubert functions, Manuscripta Math., 32, 391-405 (1980) · Zbl 0445.13008
[10] Robbiano, L.; Valla, G., On the equations defining tangent cones, (Math. Proc. Cambridge Philos. Soc., 88 (1980)), 281-297 · Zbl 0469.14001
[11] Roberts, L. G., A conjecture on Cohen-Macaulay type, C. R. Math. Rep. Acad. Sci. Canada, 3, 43-48 (1981) · Zbl 0451.14017
[12] R. Treger; R. Treger · Zbl 0474.14030
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