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A rigidity property of local cohomology modules


Authors: Enrico Sbarra and Francesco Strazzanti
Journal: Proc. Amer. Math. Soc. 145 (2017), 4099-4110
MSC (2010): Primary 13D45, 13A02; Secondary 13C13
DOI: https://doi.org/10.1090/proc/13697
Published electronically: June 16, 2017
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Abstract: The relationships between the homological properties and the invariants of $ I$, Gin$ (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
Affiliation: Dipartimento di Matematica, Università degli Studi di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
Email: enrico.sbarra@unipi.it

Francesco Strazzanti
Affiliation: Departamento de Álgebra, Facultad de Matemáticas, Universidad de Sevilla, Avda. Reina Mercedes s/n 41080 Sevilla, Spain
Email: francesco.strazzanti@gmail.com

DOI: https://doi.org/10.1090/proc/13697
Keywords: Hilbert functions, lexicographic ideals, generic initial ideals, consecutive cancellations, partially sequentially Cohen-Macaulay modules, local cohomology, Bj\"orner-Wachs polynomial.
Received by editor(s): November 9, 2015
Published electronically: June 16, 2017
Additional Notes: The first author was partially supported by PRA project 2015-16 “Geometria, Algebra e Combinatoria di Spazi di Moduli e Configurazioni”, University of Pisa.
The second author was partially supported by MTM2013-46231-P (Ministerio de Economía y Competitividad), FEDER, and the “National Group for Algebraic and Geometric Structures, and their Applications” (GNSAGA-INDAM)
Communicated by: Irena Peeva
Article copyright: © Copyright 2017 American Mathematical Society

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