Characterization of the Hilbert-Samuel polynomials of curve singularities

Juan Elias

Compositio Mathematica (1990)

  • Volume: 74, Issue: 2, page 135-155
  • ISSN: 0010-437X

How to cite

top

Elias, Juan. "Characterization of the Hilbert-Samuel polynomials of curve singularities." Compositio Mathematica 74.2 (1990): 135-155. <http://eudml.org/doc/90013>.

@article{Elias1990,
author = {Elias, Juan},
journal = {Compositio Mathematica},
keywords = {curve singularities; one-dimensional Cohen-Macaulay local ring; embedding dimension; multiplicity; reduction number; Hilbert-Samuel function},
language = {eng},
number = {2},
pages = {135-155},
publisher = {Kluwer Academic Publishers},
title = {Characterization of the Hilbert-Samuel polynomials of curve singularities},
url = {http://eudml.org/doc/90013},
volume = {74},
year = {1990},
}

TY - JOUR
AU - Elias, Juan
TI - Characterization of the Hilbert-Samuel polynomials of curve singularities
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 74
IS - 2
SP - 135
EP - 155
LA - eng
KW - curve singularities; one-dimensional Cohen-Macaulay local ring; embedding dimension; multiplicity; reduction number; Hilbert-Samuel function
UR - http://eudml.org/doc/90013
ER -

References

top
  1. [A-B] M. Auslander and D. Buchsbaum, Groups, rings, modules. Harper & Row., Publishers New York1974. Zbl0325.13001MR366959
  2. [B-S] D.A. Bayer and M. Stillman, Macaulay System and implementation. Manual 1986. 
  3. [Bu] L. Burch, On ideals of finite homological dimension in local rings. Math. Proc. Camb. Phil. Soc.64 (1968), 941-946. Zbl0172.32302MR229634
  4. [C] E. Casas, Sobre el cálculo efectivo del género de las curvas algebraicas. Collect. Math.25 (1974), 3-11. 
  5. [E-1] J. Elias, On the analytic equivalence of curves. Proc. Camb. Phil. Soc.100, 1, 57-64 (1986). Zbl0612.14020MR838653
  6. [E-2] J. Elias, A sharp bound for the minimal number of generators of perfect height two ideals. Manus. Math.55 (1986), 93-99. Zbl0588.13018MR828413
  7. [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. Zbl0673.14018MR961364
  8. [E-4] J. Elias, The Hilbert Scheme of curve singularities. Preprint. 
  9. [E-I] J. Elias, and A. Iarrobino, Extremal Gorenstein algebras of codimension three; the Hilbert function of a Cohen-Macaulay algebra. Journal of Algebra110(2) 1987, 344-356. Zbl0628.13016MR910388
  10. [E-Ch] F. Enriques and O. Chisini, Teoria geometrica delle equazione e delle funzione algebriche. Nicola Zanichelli, Bologna1918. 
  11. [E-N] J.A. Eagon and D.G. Northcott, Ideals defined by matrices and a certain complex associated with them. Proc. Royal Soc. Set.A269 (1962), 188-204. Zbl0106.25603MR142592
  12. [F-L] R. Fröberg and D. Laksov, Compressed algebras. Lecture Notes in Math. No 1092Springer Verlag, 1983). Zbl0558.13007MR775880
  13. [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. Zbl0535.13012MR724713
  14. [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. Zbl0464.14007MR618382
  15. [He] J. Herzog, Generators and relations of abelian semigroups and semigroups rings. Manus. Math.3 (1970), 175-193. Zbl0211.33801MR269762
  16. [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). Zbl0316.13011MR384785
  17. [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). Zbl0099.15702MR90850
  18. [K] D. Kirby, The reduction number of a one-dimensional local ring. J. London Math. Soc. (2) 10(1975), 471-481. Zbl0305.13017MR379483
  19. [M] E. Matlis, 1-Dimensional Cohen-Macaulay Rings. Lecture Notes in Math. No 327 (Springer Verlag, 1977). Zbl0264.13012MR357391
  20. [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. Zbl0082.03304
  21. [O-1] F. Orecchia, Generalized Hilbert functions of Cohen-Macaulay varieties. Lecture Notes in Math. No 997 (Springer Verlag, 1982). Zbl0514.14020MR714758
  22. [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). Zbl0503.13013MR686947
  23. [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). Zbl0558.14008MR686949
  24. [Ros-V] M.E. Rossi and G. Valla, Multiplicity and t-isomultiple ideals. Nagoya Math. J. Vol. 110 (1980), 81-111. Zbl0658.13018MR945908
  25. [S-1] J.D. Sally, On the associated graded ring of a local Cohen-Macaulay ring. J. Math. Kyoto Univ.17 (1977), 19-21. Zbl0353.13017MR450259
  26. [S-2] J.D. Sally, Good Embedding Dimensions for Gorenstein Singularities. Math. Ann.249 (1980), 95-106. Zbl0414.13009MR578716
  27. [S-3] J.D. Sally, Tangent cones at Gorenstein singularities. Comp. Math.40, Fasc. 2 (1980), 167-175. Zbl0389.13009MR563540
  28. [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). Zbl0395.13010MR485852
  29. [Sch] P. Schenzel, Uber die freien Auflösungen extremaler Cohen-Macaulay Ringe. J. Algebra(1980), 64, 94-101. Zbl0449.13008MR575785
  30. [St] R.P. Stanley, Hilbert functions of Graded Algebras. Adv. in Math.28 (1978), 57-83. Zbl0384.13012MR485835
  31. [V der W] B.L., Van der Waerden, Infinitely near points. Indagationes Math.12 (1950), 401-410. Zbl0038.32101

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.