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September 2012 Alternative polarizations of Borel fixed ideals
Kohji Yanagawa
Nagoya Math. J. 207: 79-93 (September 2012). DOI: 10.1215/00277630-1630032


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 S˜ such that S/I is a quotient of S˜/J by a (linear) regular sequence. We show that a Borel fixed ideal admits a nonstandard polarization. For example, while the usual polarization sends xy2S to x1y1y2S˜, 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.


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Kohji Yanagawa. "Alternative polarizations of Borel fixed ideals." Nagoya Math. J. 207 79 - 93, September 2012.


Published: September 2012
First available in Project Euclid: 26 July 2012

zbMATH: 1256.13005
MathSciNet: MR2957143
Digital Object Identifier: 10.1215/00277630-1630032

Primary: 13C13 , 13F55 , 13P05

Rights: Copyright © 2012 Editorial Board, Nagoya Mathematical Journal


Vol.207 • September 2012
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