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Number of generators of ideals

Published online by Cambridge University Press:  22 January 2016

Juan Elias ,
Lorenzo Robbiano  and
Giuseppe Valla
Juan Elias
Affiliation:
Department de Algebra i Geometria, Universitat de Barcelona, 08007 Barcelona, Spain
Lorenzo Robbiano
Affiliation:
Dipartimento di Matematica, Universita’ di Genova, Via L. B. Alberti 4 16132 Genova, Italy
Giuseppe Valla
Affiliation:
Dipartimento di Matematica, Universita’ di Genova, Via L. B. Alberti 4 16132 Genova, Italy
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Let I be a homogeneous ideal of a polynomial ring over a field, v(I) the number of elements of any minimal basis of I, e = e(I) the multiplicity or degree of R/I, h = h(I) the height or codimension of I, i = indeg (I) the initial degree of J, i.e. the minimal degree of non zero elements of I.

This paper is mainly devoted to find bounds for v(I) when I ranges over large classes of ideals. For instance we get bounds when I ranges over the set of perfect ideals with preassigned codimension and multiplicity and when I ranges over the set of perfect ideals with preassigned codimension, multiplicity and initial degree. Moreover all the bounds are sharp since they are attained by suitable ideals. Now let us make some historical remarks.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 123 , September 1991 , pp. 39 - 76
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

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