Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 39, No. 2, pp. 433-446 (1998)

On the Cohen-Macaulayness of the Associated Graded Ring of Certain Monomial Curves

S. Molinelli, D. P. Patil, G. Tamone

Dipartimento di Matematica, Universita di Genova, via Dodecaneso 35, I-16146 Genova, Italy, e-mail:,

Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India, e-mail:

Abstract: \font\bbb=msbm10 \font\euei=eufm8 \font\calf=cmsy10 \def\cal#1{\hbox{\calf #1}} Let $K$ be a field and let $m_{0},\ldots,m_{e-1}$ be a sequence of positive integers. Let $\cal C$ be an algebroid monomial curve in the affine $e$-space $\hbox{\bbb A}_{K}^{e}$ defined parametrically by $X_{0}=T^{m_{0}},\ldots,X_{e-1}=T^{m_{e-1}}$ and let $A$ be the coordinate ring of $\cal C$. In this paper we discuss when exactly the associated graded ring $ gr_{\hbox{\euei m}}(A)$ is Cohen-Macaulay. If some $e-1$ terms of $m_{0},\ldots,m_{e-1}$ form an arithmetic sequence then we give necessary and sufficient conditions for the Cohen-Macaulayness of the associated graded ring $ gr_{\hbox{\euei m}}(A)$.

Full text of the article:

[Previous Article] [Next Article] [Contents of this Number]