Nagoya Mathematical Journal

Alternative polarizations of Borel fixed ideals

Kohji Yanagawa

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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 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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Nagoya Math. J., Volume 207 (2012), 79-93.

First available in Project Euclid: 26 July 2012

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Zentralblatt MATH identifier

Primary: 13C13: Other special types 13P05: Polynomials, factorization [See also 12Y05] 13F55: Stanley-Reisner face rings; simplicial complexes [See also 55U10]


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

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