Dipartimento di Matematica, Universita di Genova, via Dodecaneso 35, I-16146 Genova, Italy, e-mail: tamone@dima.unige.it, molinell@.dima.unige.itDepartment of Mathematics, Indian Institute of Science, Bangalore 560 012, India, e-mail: patil@math.iisc.ernet.in
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)$.
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