The converse of a theorem by Bayer and Stillman

2014/10/22 by Loh, HyunBin
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1410.5969

Abstract

Bayer-Stillman showed that reg(I) = reg(gin_τ(I)) when τ is the graded reverse lexicographic order. We show that the reverse lexicographic order is the unique monomial order τ satisfying reg(I) = reg(gin_τ(I)) for all ideals I. We also show that if gin_τ1(I) = gin_τ2(I) for all I, then τ₁ = τ₂.

Related

• Distinct monomial orders with same induced orderings
• Evaluations of initial ideals and Castelnuovo-Mumford regularity
• Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic
• Generic ideals and Moreno-Soc'ıas conjecture
• Reverse Lexicographic and Lexicographic Shifting