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arXiv · 0705.3767

Contracted ideals and the Groebner fan of the rational normal curve

Aldo Conca·Emanuela De Negri·Maria Evelina Rossi
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Abstract

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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Aldo Conca, Emanuela De Negri, Maria Evelina Rossi. 2007-10-11. Contracted ideals and the Groebner fan of the rational normal curve. https://arxiv.org/abs/0705.3767

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