Combinatorial characterizations of generalized Cohen-Macaulay monomial ideals
Yukihide Takayama
TL;DR
This paper extends Hochster's formula to non-square-free monomial ideals, enabling combinatorial characterizations of generalized Cohen-Macaulay monomial ideals and exploring further applications of the generalized formula.
Contribution
It introduces a generalized Hochster's formula for monomial ideals beyond the square-free case, providing new combinatorial characterizations.
Findings
Generalized Hochster's formula for monomial ideals
Characterization of generalized Cohen-Macaulay monomial ideals
Additional applications of the generalized formula
Abstract
We give a generalization of Hochster's formula for local cohomologies of square-free monomial ideals to monomial ideals, which are not necessarily square-free. Using this formula, we give combinatorial characterizations of generalized Cohen-Macaulay monomial ideals. We also give other applications of the generalized Hochster's formula.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Advanced Combinatorial Mathematics · Topological and Geometric Data Analysis