Maximal and Cohen-Macaulay projective monomial curves

Abstract

In this paper we continue the investigation of Cohen-Macaulay projective monomial curves begun in [Les Reid, Leslie G. Roberts, Non-Cohen-Macaulay projective monomial curves, J. Algebra 291 (2005) 171-186]. In the process we introduce maximal curves. Cohen-Macaulay curves are maximal, but not conversely. We show that the number of all curves of degree d that are Cohen-Macaulay grows exponentially, but not as fast as the total number of curves, and also that maximal curves of degree d with sufficiently large embedding dimension relative to d are Cohen-Macaulay.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1016/j.jalgebra.2006.04.014

Publication Date

1-1-2007

Journal Title

Journal of Algebra

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