Bekir DANIŞ

A short note on generic initial ideals

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

The definition of a generic initial ideal includes the assumption x1 > x2 > · · · > xn . A natural question is how generic initial ideals change when we permute the variables. In the article [1, §2], it is shown that the generic initial ideals are permuted in the same way when the variables in the monomial order are permuted. We give a different proof of this theorem. Along the way, we study the Zariski open sets which play an essential role in the definition of a generic initial ideal and also prove a result on how the Zariski open set changes after a permutation of the variables.

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[1] Danış B, Sezer M. Generic initial ideals of modular polynomial invariants. Journal of Pure and Applied Algebra 2020; 224 (6). doi: 10.1016/j.jpaa.2019.106255
[2] Eisenbud D. Commutative Algebra with a View Toward Algebraic Geometry. New York, NY, USA: Springer-Verlag, 1995.
[3] Green ML. Generic initial ideals. In: Elias J, Giral JM, Mió-Roig RM, Zarzuela S. Six Lectures on Commutative Algebra. Basel, Switzerland: Birkhäuser, 1998, pp. 119-186.
[4] Herzog J, Hibi T. Monomial Ideals. London, England: Springer-Verlag London Limited, 2011.