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Ideals with Trivial Conormal Bundle

Published online by Cambridge University Press:  20 November 2018

A. V. Geramita  and
C. A. Weibel
A. V. Geramita
Affiliation:
Queen's University, Kingston, Ontario
C. A. Weibel
Affiliation:
Queen's University, Kingston, Ontario
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Throughout this paper all rings considered will be commutative, noetherian with identity. If R is such a ring and M is a finitely generated R-module, we shall use v(M) to denote that non-negative integer with the property that M can be generated by v(M) elements but not by fewer.

Since every ideal in a noetherian ring is finitely generated, it is a natural question to ask what v(I) is for a given ideal I. Hilbert's Nullstellensatz may be viewed as the first general theorem dealing with this question, answering it when I is a maximal ideal in a polynomial ring over an algebraically closed field.

More recently, it has been noticed that the properties of an R-ideal I are intertwined with those of the R-module I/I2.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 1 , 01 February 1980 , pp. 210 - 218
Copyright
Copyright © Canadian Mathematical Society 1980

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