The relationships between the homological properties and the invariants of I, Gin(I) and I^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.
Sbarra E, Strazzanti F (2017). A rigidity property of local cohomology modules. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 145(10), 4099-4110 [10.1090/proc/13697].
A rigidity property of local cohomology modules
Strazzanti F
2017
Abstract
The relationships between the homological properties and the invariants of I, Gin(I) and I^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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
