A rigidity property of local cohomology modules
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- by Enrico Sbarra and Francesco Strazzanti PDF
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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.References
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Additional Information
- 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
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 4099-4110
- MSC (2010): Primary 13D45, 13A02; Secondary 13C13
- DOI: https://doi.org/10.1090/proc/13697
- MathSciNet review: 3690597