Abstract
Consider the subring of , where k is a field and x, y indeterminates over k. We calculate the Hilbert polynomial of . The multiplicity of this ideal provides part of a criterion for the ring to be Cohen-Macaulay. Next, we prove a simple numerical criterion for R to be Cohen-Macaulay in the case when t = 2. We also provide a simple algorithm which identifies the monomial k-basis of . Finally, these methods are specialized to the case of projective monomial curves in .
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