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Gröbner Flags and Gorenstein Algebras

Published online by Cambridge University Press:  04 December 2007

Aldo Conca ,
Maria Evelina Rossi  and
Giuseppe Valla
Aldo Conca
Affiliation:
Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16132 Genova, Italy. E-mail: conca@dima.unige.it
Maria Evelina Rossi
Affiliation:
Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16132 Genova, Italy. E-mail: rossim@dima.unige.it
Giuseppe Valla
Affiliation:
Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16132 Genova, Italy. E-mail: valla@dima.unige.it
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Abstract

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The goal of this paper is to study the Koszul property and the property of having a Gröbner basis of quadrics for classical varieties and algebras as canonical curves, finite sets of points and Artinian Gorenstein algebras with socle in low degree. Our approach is based on the notion of Gröbner flags and Koszul filtrations. The main results are the existence of a Gröbner basis of quadrics for the ideal of the canonical curve whenever it is defined by quadrics, the existence of a Gröbner basis of quadrics for the defining ideal of s [les ] 2n points in general linear position in Pn, and the Koszul property of the ‘generic’ Artinian Gorenstein algebra of socle degree 3.

Keywords

resolutionsKoszul algebrasGröbner bases of quadricscanonical curvesArtinian Gorenstein algebras
Type
Research Article
Information
Compositio Mathematica , Volume 129 , Issue 1 , October 2001 , pp. 95 - 121
Copyright
© 2001 Kluwer Academic Publishers