Contracted ideals and the Gröbner fan of the rational normal curve

Conca, Aldo; De Negri, Emanuela; Rossi, Maria Evelina

doi:10.2140/ant.2007.1.239

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Contracted ideals and the Gröbner fan of the rational normal curve

Aldo Conca, Emanuela De Negri and Maria Evelina Rossi

Vol. 1 (2007), No. 3, 239–268

DOI: 10.2140/ant.2007.1.239

Abstract

The paper has two goals: the study of the associated graded ring of contracted homogeneous ideals in $K [x, y]$ and the study of the Gröbner fan of the ideal $P$ of the rational normal curve in $ℙ^{d}$ . These two problems are, quite surprisingly, very tightly related. We completely classify the contracted ideals with Cohen–Macaulay associated graded ring in terms of the numerical invariants arising from Zariski’s factorization. We determine explicitly the initial ideals (monomial or not) of $P$ , that are Cohen–Macaulay.

Keywords

Gröbner fan, contracted ideal, Rees algebra, rational normal curve, Cohen–Macaulay ring

Mathematical Subject Classification 2000

Primary: 13A30

Secondary: 13P10, 13D40

Milestones

Received: 1 February 2007

Revised: 27 August 2007

Accepted: 29 September 2007

Published: 1 August 2007

Authors

Aldo Conca
Dipartimento di Matematica Università di Genova Via Dodecaneso 35 I-16146 Genova Italy

Emanuela De Negri
Dipartimento di Matematica Università di Genova Via Dodecaneso 35 I-16146 Genova Italy

Maria Evelina Rossi
Dipartimento di Matematica Università di Genova Via Dodecaneso 35 I-16146 Genova Italy

Vol. 1, No. 3, 2007