A rigidity property of local cohomology modules

Sbarra, Enrico; Strazzanti, Francesco

doi:10.1090/proc/13697

A rigidity property of local cohomology modules
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by Enrico Sbarra and Francesco Strazzanti PDF

Proc. Amer. Math. Soc. 145 (2017), 4099-4110 Request permission

Abstract:

The relationships between the homological properties and the invariants of $I$, Gin$(I)$ and $I^\textrm { lex}$ 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.

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