Characterization of the Hilbert-Samuel polynomials of curve singularities
Compositio Mathematica, Tome 74 (1990) no. 2, pp. 135-155. 
@article{CM_1990__74_2_135_0,
     author = {Elias, Juan},
     title = {Characterization of the {Hilbert-Samuel} polynomials of curve singularities},
     journal = {Compositio Mathematica},
     pages = {135--155},
     publisher = {Kluwer Academic Publishers},
     volume = {74},
     number = {2},
     year = {1990},
     mrnumber = {1047736},
     zbl = {0724.13021},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1990__74_2_135_0/}
}
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Elias, Juan. Characterization of the Hilbert-Samuel polynomials of curve singularities. Compositio Mathematica, Tome 74 (1990) no. 2, pp. 135-155. http://archive.numdam.org/item/CM_1990__74_2_135_0/

[A-B] M. Auslander and D. Buchsbaum, Groups, rings, modules. Harper & Row., Publishers New York 1974. | MR | Zbl

[B-S] D.A. Bayer and M. Stillman, Macaulay System and implementation. Manual 1986.

[Bu] L. Burch, On ideals of finite homological dimension in local rings. Math. Proc. Camb. Phil. Soc. 64 (1968), 941-946. | MR | Zbl

[C] E. Casas, Sobre el cálculo efectivo del género de las curvas algebraicas. Collect. Math. 25 (1974), 3-11.

[E-1] J. Elias, On the analytic equivalence of curves. Proc. Camb. Phil. Soc. 100, 1, 57-64 (1986). | MR | Zbl

[E-2] J. Elias, A sharp bound for the minimal number of generators of perfect height two ideals. Manus. Math. 55 (1986), 93-99. | MR | Zbl

[E-3] J. Elias, An upper bound of the singularity order for the generic projection. J. of Pure and Appl. Algebra. 53 (1988) 267-270. | MR | Zbl

[E-4] J. Elias, The Hilbert Scheme of curve singularities. Preprint.

[E-I] J. Elias, and A. Iarrobino, Extremal Gorenstein algebras of codimension three; the Hilbert function of a Cohen-Macaulay algebra. Journal of Algebra 110(2) 1987, 344-356. | MR | Zbl

[E-Ch] F. Enriques and O. Chisini, Teoria geometrica delle equazione e delle funzione algebriche. Nicola Zanichelli, Bologna 1918.

[E-N] J.A. Eagon and D.G. Northcott, Ideals defined by matrices and a certain complex associated with them. Proc. Royal Soc. Set. A 269 (1962), 188-204. | MR | Zbl

[F-L] R. Fröberg and D. Laksov, Compressed algebras. Lecture Notes in Math. No 1092 Springer Verlag, 1983). | MR | Zbl

[G-M-R] A.V., Geramita, P. Maroscia and L. Roberts. The Hilbert function of a reduced k-algebra. J. London Math. Soc (2), 28 (1983), 443-452. | MR | Zbl

[G-O] A.V. Geramita and F. Orecchia, On the Cohen-Macaulay Type of s-Lines in An. Journal of Algebra. 70 (1981), 116-140. | MR | Zbl

[He] J. Herzog, Generators and relations of abelian semigroups and semigroups rings. Manus. Math. 3 (1970), 175-193. | EuDML | MR | Zbl

[HW] J. Herzog, and Waldi. A note on the Hilbert function of a one dimensional Cohen-Macaulay local ring. Manus. Math. 16, 251-260 (1975). | EuDML | MR | Zbl

[H] H. Hironaka, On the arithmetic genera and the effective genera of algebraic curves. Memoirs of the College of Sciences, Univ. Tokio, Ser. A, Vol. XXX, Math. No 2 (1957). | MR | Zbl

[K] D. Kirby, The reduction number of a one-dimensional local ring. J. London Math. Soc. (2) 10(1975), 471-481. | MR | Zbl

[M] E. Matlis, 1-Dimensional Cohen-Macaulay Rings. Lecture Notes in Math. No 327 (Springer Verlag, 1977). | MR | Zbl

[N] D.G. Northcott, On the notion of a first neighbourhood ring with an application to the AF + Bϕ theorem. Math. Proc. Camb. Phil. Soc. 53 (1957), 43-56. | Zbl

[O-1] F. Orecchia, Generalized Hilbert functions of Cohen-Macaulay varieties. Lecture Notes in Math. No 997 (Springer Verlag, 1982). | MR | Zbl

[O-2] F. Orecchia, Maximal Hilbert functions of a one-dimensional local rings. Lecture Notes in Pure and Appl. Math. Series, 84 (Marcel Dekker, 1983). | MR | Zbl

[Rob-V] L. Robbiano and G. Valla, Free resolutions of special tangent cones. Commutative Algebra. Lecture Notes in Pure and Appl. Math. Series, 84. (Marcel Dekker, 1983). | MR | Zbl

[Ros-V] M.E. Rossi and G. Valla, Multiplicity and t-isomultiple ideals. Nagoya Math. J. Vol. 110 (1980), 81-111. | MR | Zbl

[S-1] J.D. Sally, On the associated graded ring of a local Cohen-Macaulay ring. J. Math. Kyoto Univ. 17 (1977), 19-21. | MR | Zbl

[S-2] J.D. Sally, Good Embedding Dimensions for Gorenstein Singularities. Math. Ann. 249 (1980), 95-106. | EuDML | MR | Zbl

[S-3] J.D. Sally, Tangent cones at Gorenstein singularities. Comp. Math. 40, Fasc. 2 (1980), 167-175. | EuDML | Numdam | MR | Zbl

[S-4] J.D. Sally, Number of generators of ideals in local rings. Lecture Notes in Pure and Applied Math. Series, 35 (Marcel Dekker, 1978). | MR | Zbl

[Sch] P. Schenzel, Uber die freien Auflösungen extremaler Cohen-Macaulay Ringe. J. Algebra(1980), 64, 94-101. | MR | Zbl

[St] R.P. Stanley, Hilbert functions of Graded Algebras. Adv. in Math. 28 (1978), 57-83. | MR | Zbl

[V der W] B.L., Van Der Waerden, Infinitely near points. Indagationes Math. 12 (1950), 401-410. | Zbl