Contracted ideals and the Groebner fan of the rational normal curve

Details Contracted ideals and the Groebner fan of the rational normal curve Contracted ideals and the Groebner fan of the rational normal curve

2007-05-25

arxiv.org/abs/0705.3767v2

Mathematics

Commutative Algebra

revised version, references added. To appear in ``Algebra and Number Theory"

Scientific paper

The 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.

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