Maximal and Cohen-Macaulay projective monomial curves
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.
Reid, Les, and Leslie G. Roberts. "Maximal and Cohen–Macaulay projective monomial curves." Journal of Algebra 307, no. 1 (2007): 409-423.
Journal of Algebra