Componentwise Linearity Under Square-Free Gröbner Degenerations

2023/03/09 by Yu, Hongmiao
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.05190

Abstract

Using the recent results on square-free Gröbner degenerations by Conca and Varbaro, we proved that if a homogeneous ideal I of a polynomial ring is such that its initial ideal in_<(I) is square-free and β₀(I) = β₀(in_<(I)), then I is a componentwise linear ideal if and only if in_<(I) is a componentwise linear ideal. In particular, if furthermore one of I and in_<(I) is componentwise linear, then their graded Betti numbers coincide.

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• Square-free Groebner degenerations
• Some families of componentwise linear monomial ideals
• Componentwise linear powers and the x-condition
• Componentwise Linear Ideals From Sums
• Powers of componentwise linear ideals: The Herzog--Hibi--Ohsugi Conjecture and related problems