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Original Articles

Perron Transforms

Pages 2003-2045 | Received 21 Oct 2011, Published online: 16 Jan 2014
 

Abstract

We generalize Zariski's Perron transforms to obtain a proof of local uniformization of an arbitrary singular variety of characteristic zero along a valuation of arbitrary rank. Furthermore, we resolve the centers of all the composite valuations as well as the prime ideals of infinite value.

2010 Mathematics Subject Classification:

ACKNOWLEDGMENTS

The author sincerely thanks Cutkosky for suggesting the problem and for many helpful discussions concerning the material in this article. The author would like to thank the referee for all the suggestions and insightful remarks.

Notes

Communicated by I. Swanson.

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