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The deformation multiplicity of a map germ with respect to a Boardman symbol

Published online by Cambridge University Press:  12 July 2007

C. Bivià-Ausina  and
J. J. Nuño-Ballesteros
C. Bivià-Ausina
Affiliation:
Departament de Geometria i Topologia, Universitat de Valéncia, Campus de Burjassot, 46100 Burjassot, Spain ([email protected]; [email protected])
J. J. Nuño-Ballesteros
Affiliation:
Departament de Geometria i Topologia, Universitat de Valéncia, Campus de Burjassot, 46100 Burjassot, Spain ([email protected]; [email protected])
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Abstract

We define the deformation multiplicity of a map germ f: (Cn, 0) → (Cp, 0) with respect to a Boardman symbol i of codimension less than or equal to n and establish a geometrical interpretation of this number in terms of the set of Σi points that appear in a generic deformation of f. Moreover, this number is equal to the algebraic multiplicity of f with respect to i when the corresponding associated ring is Cohen-Macaulay. Finally, we study how algebraic multiplicity behaves with weighted homogeneous map germs.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 5 , October 2001 , pp. 1003 - 1022
Copyright
Copyright © Royal Society of Edinburgh 2001

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