2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139693The paper has two goals: the study the associated graded ring of contracted homogeneous ideals in $K[x,y]$ and the study of the Groebner fan of the ideal $P$ of the rational normal curve in ${\bf P}^d$. These two problems are, quite surprisingly, very tightly related. We completely classify the contracted ideals with a Cohen-Macaulay associated graded rings in terms of the numerical invariants arising from Zariski's factorization. We determine explicitly all the initial ideals (monomial or not) of $P$ that are Cohen-Macaulay.revised version, references added. To appear in ``Algebra and Number Theory"Commutative AlgebraCombinatorics13A30, 13P10, 13D40,text