Non-Cohen-Macaulay projective monomial curves

Abstract

We compare several ways of describing how far the homogeneous coordinate ring of a projective monomial curve is from being Cohen-Macaulay. We give a number of examples and then use these ideas to show that the fraction of projective monomial curves of a given degree that are Cohen-Macaulay approaches zero as the degree goes to infinity.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1016/j.jalgebra.2005.05.024

Publication Date

2005

Journal Title

Journal of Algebra

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