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A MIXED MULTIPLICITY FORMULA FOR COMPLETE IDEALS IN 2-DIMENSIONAL RATIONAL SINGULARITIES
VERONIQUE VAN LIERDE
Proceedings of the American Mathematical Society
Vol. 138, No. 12 (DECEMBER 2010), pp. 4197-4204
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/41059157
Page Count: 8
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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).
Proceedings of the American Mathematical Society © 2010 American Mathematical Society