Classification of Cohen-Macaulay modules of covariants for systems of binary forms

Broer, Bram

doi:10.1090/S0002-9939-1994-1189743-X

Classification of Cohen-Macaulay modules of covariants for systems of binary forms
HTML articles powered by AMS MathViewer

by Bram Broer PDF

Proc. Amer. Math. Soc. 120 (1994), 37-45 Request permission

Abstract:

For every module of covariants for a system of binary forms a formula is given, measuring to what extent Stanley’s functional equation fails to be satisfied. As an application a new proof is given for the classification of the Cohen-Macaulay modules of covariants for systems of binary forms.

References

A converse to Stanley’s conjecture for

Michel Van den Bergh, Cohen-Macaulayness of modules of covariants, Invent. Math. 106 (1991), no. 2, 389–409. MR 1128219, DOI 10.1007/BF01243917
Bram Broer, On the generating functions associated to a system of binary forms, Indag. Math. (N.S.) 1 (1990), no. 1, 15–25. MR 1054762, DOI 10.1016/0019-3577(90)90029-M
Michel Brion, Sur les modules de covariants, Ann. Sci. École Norm. Sup. (4) 26 (1993), no. 1, 1–21 (French, with English and French summaries). MR 1209911
E. Graham Evans and Phillip Griffith, Syzygies, London Mathematical Society Lecture Note Series, vol. 106, Cambridge University Press, Cambridge, 1985. MR 811636, DOI 10.1017/CBO9781107325661
Shiro Goto and Keiichi Watanabe, On graded rings. I, J. Math. Soc. Japan 30 (1978), no. 2, 179–213. MR 494707, DOI 10.2969/jmsj/03020179
Melvin Hochster and Joel L. Roberts, Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay, Advances in Math. 13 (1974), 115–175. MR 347810, DOI 10.1016/0001-8708(74)90067-X
Gerald W. Schwarz, Representations of simple Lie groups with a free module of covariants, Invent. Math. 50 (1978/79), no. 1, 1–12. MR 516601, DOI 10.1007/BF01406465
Hanspeter Kraft, Peter Slodowy, and Tonny A. Springer (eds.), Algebraische Transformationsgruppen und Invariantentheorie, DMV Seminar, vol. 13, Birkhäuser Verlag, Basel, 1989 (German). MR 1044582, DOI 10.1007/978-3-0348-7662-9
Richard P. Stanley, Combinatorics and invariant theory, Relations between combinatorics and other parts of mathematics (Proc. Sympos. Pure Math., Ohio State Univ., Columbus, Ohio, 1978) Proc. Sympos. Pure Math., XXXIV, Amer. Math. Soc., Providence, R.I., 1979, pp. 345–355. MR 525334