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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An iterative construction of Gorenstein ideals


Authors: C. Bocci, G. Dalzotto, R. Notari and M. L. Spreafico
Journal: Trans. Amer. Math. Soc. 357 (2005), 1417-1444
MSC (2000): Primary 14M05, 13H10; Secondary 14M06, 13D02, 18G10
Published electronically: July 22, 2004
MathSciNet review: 2115371
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Abstract: In this paper, we present a method to inductively construct Gorenstein ideals of any codimension $ c.$ We start from a Gorenstein ideal $ I $ of codimension $ c $ contained in a complete intersection ideal $ J $ of the same codimension, and we prove that under suitable hypotheses there exists a new Gorenstein ideal contained in the residual ideal $ I : J.$ We compare some numerical data of the starting and the resulting Gorenstein ideals of the construction. We compare also the Buchsbaum-Eisenbud matrices of the two ideals, in the codimension three case. Furthermore, we show that this construction is independent from the other known geometrical constructions of Gorenstein ideals, providing examples.


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Additional Information

C. Bocci
Affiliation: Dipartimento di Matematica, Università di Torino, I-10123 Torino, Italy
Address at time of publication: Dipartimento di Matematica, Università di Milano, I-20133 Milano, Italy
Email: bocci@dm.unito.it, cristiano.bocci@unimi.it

G. Dalzotto
Affiliation: Dipartimento di Matematica, Università di Genova, I-16146 Genova, Italy
Address at time of publication: Dipartimento di Matematica, Università di Pisa, I-56127 Pisa, Italy
Email: dalzotto@module.dima.unige.it, dalzotto@mail.dm.unipi.it

R. Notari
Affiliation: Dipartimento di Matematica, Politecnico di Torino, I-10129 Torino, Italy
Email: roberto.notari@polito.it

M. L. Spreafico
Affiliation: Dipartimento di Matematica, Politecnico di Torino, I-10129 Torino, Italy
Email: maria.spreafico@polito.it

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03521-4
PII: S 0002-9947(04)03521-4
Received by editor(s): February 24, 2003
Received by editor(s) in revised form: September 26, 2003
Published electronically: July 22, 2004
Article copyright: © Copyright 2004 American Mathematical Society