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Alternative polarizations of Borel fixed ideals

Published online by Cambridge University Press:  11 January 2016

Kohji Yanagawa
Kohji Yanagawa*
Affiliation:
Department of Mathematics, Kansai University, Suita 564-8680, Japan, [email protected]
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Abstract

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For a monomial ideal I of a polynomial ring S, a polarization of I is a square-free monomial ideal J of a larger polynomial ring such that S/I is a quotient of /J by a (linear) regular sequence. We show that a Borel fixed ideal admits a nonstandard polarization. For example, while the usual polarization sends ours sends it to x1y2y3 Using this idea, we recover/refine the results on square-free operation in the shifting theory of simplicial complexes. The present paper generalizes a result of Nagel and Reiner, although our approach is very different.

Keywords

13C1313P0513F55
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 207 , September 2012 , pp. 79 - 93
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2012

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