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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

A mixed multiplicity formula for complete ideals in $ 2$-dimensional rational singularities


Author: Veronique Van Lierde
Journal: Proc. Amer. Math. Soc. 138 (2010), 4197-4204
MSC (2010): Primary 13B22, 13H15
Published electronically: June 29, 2010
MathSciNet review: 2680046
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Abstract: Let $ (R,m)$ be a 2-dimensional rational singularity with algebraically closed residue field and for which the associated graded ring is an integrally closed domain. We use the work of Göhner on condition $ (N)$ and the theory of degree functions developed by Rees and Sharp to give a very short and elementary proof of a formula for the (mixed) multiplicity of complete $ m$-primary ideals in $ (R,m)$.


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Additional Information

Veronique Van Lierde
Affiliation: School of Science and Engineering, Al Akhawayn University, Ifrane 53000, Morocco
Email: v.lierde@aui.ma

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10455-0
Keywords: Degree function, quadratic transformation, 2-dimensional rational singularity, complete ideal, mixed multiplicity
Received by editor(s): April 18, 2009
Received by editor(s) in revised form: February 20, 2010
Published electronically: June 29, 2010
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.