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arXiv · 1511.02755

A rigidity property of local cohomology modules

Enrico Sbarra·Francesco Strazzanti
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Abstract

The relationships between the invariants and the homological properties of $I$, ${\rm Gin}(I)$ and $I^{\rm lex}$ 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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Enrico Sbarra, Francesco Strazzanti. 2015-11-09. A rigidity property of local cohomology modules. https://arxiv.org/abs/1511.02755

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