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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
Stable URL: http://www.jstor.org/stable/41059157
Page Count: 8
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A MIXED MULTIPLICITY FORMULA FOR COMPLETE IDEALS IN 2-DIMENSIONAL RATIONAL SINGULARITIES
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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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