Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T23:57:31.329Z Has data issue: false hasContentIssue false

Symmetric ladders

Published online by Cambridge University Press:  22 January 2016

Aldo Conca*
Affiliation:
FB6 Mathematik una Informatik, Universität GHS Essen, 45117 Essen, Germany
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we define and study ladder determinantal rings of a symmetric matrix of indeterminates. We show that they are Cohen-Macaulay domains. We give a combinatorial characterization of their h-vectors and we compute the a-invariant of the classical determinantal rings of a symmetric matrix of indeterminates.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1994

References

[1] Abhyankar, S. S., Enumerative combinatorics of Young tableaux, Marcel Dekker, New York, 1988.Google Scholar
[2] Abhyankar, S. S., Kulkarni, D. M., On Hilbertian ideals, Linear Algabra and its Appl., 116 (1989), 5379.Google Scholar
[3] Barile, M., The Cohen-Macaulayness and the a-invariant of an algebra with straightening law on a doset, Comm. in Alg., 22 (1994), 413430.Google Scholar
[4] Björner, A., Shellable and Cohen-Macaulay partially ordered sets, Trans. Amer. Math. Soc., 260 (1980), 159183.Google Scholar
[5] Bruns, W., Herzog, J., On the computation of a-invariants, Manuscripta Math., 77 (1992), 201213.Google Scholar
[6] Bruns, W., Herzog, J., Vetter, U., Syzygies and walks, to appear in the Proc. of the Workshop in Comm. Alg. Trieste 1992.Google Scholar
[7] Bruns, W., Vetter, U., Determinantal rings, Lect. Notes Math. 1327, Springer, Heidelberg, 1988.Google Scholar
[8] Conca, A., Gröbner bases of ideals of minors of a symmetric matrix, J. of Alg., 166 (1994), 406421.CrossRefGoogle Scholar
[9] Conca, A., Ladder determinantal rings, to appear in J. of Pure and Appl. Alg.Google Scholar
[10] Conca, A., Divisor class group and canonical class of determinantal rings defined by ideals of minors of a symmetric matrix, Arch. Mat. 63 (1994), 216224.CrossRefGoogle Scholar
[11] Conca, A., Herzog, J., On the Hilbert function of determinantal rings and their canonical module, to appear in Proc. Amer Math. Soc.Google Scholar
[12] De Concini, C., Eisenbud, D., Procesi, C., Hodge algebras, Asterisque 91, 1982.Google Scholar
[13] Goto, S., On the Gorensteinness of determinantal loci, J. Math. Kyoto Univ., 19 (1979), 371374.Google Scholar
[14] Gräbe, H. G., Streckungsringe, Dissertation B, Pädagogische Hochschule Erfurt, 1988.Google Scholar
[15] Herzog, J., Trung, N. V., Gröbner bases and multiplicity of determinantal and pfaffian ideals, Adv. Math., 96 (1992), 137.CrossRefGoogle Scholar
[16] Kutz, R., Cohen-Macaulay rings and ideal theory in rings of invariants of algebraic groups, Trans. Amer. Math. Soc., 194 (1974), 115129.Google Scholar
[17] Narasimhan, H., The irreducibility of ladder determinantal varieties, J. Alg., 102 (1986), 162185.Google Scholar
[18] Stanley, R., Combinatorics and Commutative Algebra, Birkhäuser, Basel, 1983.CrossRefGoogle Scholar
[19] Stanley, R., Enumerative Combinatorics I, Wardworth and Brook, California, 1986.Google Scholar