Combinatorial characterizations of generalized Cohen-Macaulay monomial ideals

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.

This is a largely enhanced version of the previous manuscript "A generalized Hochster's formula for local cohomologies of monomial ideals"

Cited by in corpus (27)

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• Geometric regularity of powers of two-dimensional squarefree monomial ideals
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• Locally complete intersection Stanley-Reisner ideals
• Notes on C-graded modules over an affine semigroup ring K[C]
• Combinatorial characterizations of the saturation and the associated primes of the fourth power of edge ideals
• Local Cohomology and Degree Complexes of Monomial Ideals
• Integral closure of small powers of edge ideals and their regularity
• Comparision between regularity of small symbolic powers and ordinary powers of an edge ideal
• Simplicial complexes with rigid depth
• Rees algebras and generalized depth-like conditions in prime characteristic
• $a_i$-invariants of powers of ideals
• On the depth and Stanley depth of integral closure of powers of monomial ideals
• On the second powers of Stanley-Reisner ideals
• Combinatorial characterizations of the Cohen-Macaulayness of the second power of edge ideals
• Behavior of local cohomology modules under polarization
• Tameness of Local cohomology of monomial ideals with respect to monomial prime ideals
• On the associated primes and the depth of the second power of squarefree monomial ideals
• A-graded methods for monomial ideals
• Regularity of Canonical and Deficiency modules for Monomial ideals
• Generalized complete intersections with linear resolutions
• Stanley-Reisner ideals whose powers have finite length cohomologies
• Regularity of symbolic powers of square-free monomial ideals