Contracted ideals and the Groebner fan of the rational normal curve

2007/05/25 by Aldo Conca, Conca, Aldo, Emanuela De Negri +3 · 1 citation
Computer Science · Mathematics · Medicine · #13A30 #13D40 #13P10 #Cancer Treatment and Pharmacology #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0705.3767

openalex publication_date 2007/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Smooth Herzog projective curves

Related

• Graded rings associated with contracted ideals
• A Minimal Groebner Basis for the Defining Ideals of Certain Affine Monomial Curves
• Generalized stretched ideals and Sally Conjecture
• Groebner bases, monomial group actions, and the Cox rings of Del Pezzo surfaces
• Integrally closed and componentwise linear ideals