Bounds for the Betti numbers of generalized Cohen-Macaulay ideals

Hoa, Lê Tuan; Miró-Roig, Rosa M.

doi:10.1090/S0002-9939-1995-1254842-1

Bounds for the Betti numbers of generalized Cohen-Macaulay ideals
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by Lê Tuan Hoa and Rosa M. Miró-Roig

Proc. Amer. Math. Soc. 123 (1995), 2397-2405

DOI: https://doi.org/10.1090/S0002-9939-1995-1254842-1

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Abstract:

Upper bounds for the Betti numbers of generalized Cohen-Macaulay ideals are given. In particular, for the case of non-degenerate, reduced and irreducible projective curves we get an upper bound which only depends on their degree.

References

Shalom Eliahou and Michel Kervaire, Minimal resolutions of some monomial ideals, J. Algebra 129 (1990), no. 1, 1–25. MR 1037391, DOI 10.1016/0021-8693(90)90237-I
Juan Elías, Lorenzo Robbiano, and Giuseppe Valla, Number of generators of ideals, Nagoya Math. J. 123 (1991), 39–76. MR 1126182, DOI 10.1017/S0027763000003640
L. Gruson, R. Lazarsfeld, and C. Peskine, On a theorem of Castelnuovo, and the equations defining space curves, Invent. Math. 72 (1983), no. 3, 491–506. MR 704401, DOI 10.1007/BF01398398
Lê Tuấn Hoa, Bounds for the number of generators of generalized Cohen-Macaulay ideals, J. Algebra 178 (1995), no. 1, 302–316. MR 1358268, DOI 10.1006/jabr.1995.1351
Le Tuan Hoa, Jürgen Stückrad, and Wolfgang Vogel, Towards a structure theory for projective varieties of $\textrm {degree}=\textrm {codimension}+2$, J. Pure Appl. Algebra 71 (1991), no. 2-3, 203–231. MR 1117635, DOI 10.1016/0022-4049(91)90148-U
Judith D. Sally, Numbers of generators of ideals in local rings, Marcel Dekker, Inc., New York-Basel, 1978. MR 0485852
Jürgen Stückrad and Wolfgang Vogel, Buchsbaum rings and applications, Springer-Verlag, Berlin, 1986. An interaction between algebra, geometry and topology. MR 881220, DOI 10.1007/978-3-662-02500-0
G. Valla, On the Betti numbers of perfect ideals, Compositio Math. 91 (1994), no. 3, 305–319. MR 1273653