A rigidity property of local cohomology modules

Abstract

The relationships between the invariants and the homological properties of $I$, $\mathrm{Gin}(I)$ and $I^{\mathrm{lex}}$ have been studied extensively over the past decades. A result of A. Conca, J. Herzog and T. Hibi points out some rigid behaviours of their Betti numbers. In this work we establish a local cohomology counterpart of their theorem. To this end, we make use of properties of sequentially Cohen-Macaulay modules and we study a generalization of such concept by introducing what we call partially sequentially Cohen-Macaulay modules, which might be of interest by themselves.

References in corpus (1)

• Ideals with maximal local cohomology modules