Lyubeznik numbers of monomial ideals
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- by Josep Àlvarez Montaner and Alireza Vahidi PDF
- Trans. Amer. Math. Soc. 366 (2014), 1829-1855 Request permission
Abstract:
Let $R=k[x_1,...,x_n]$ be the polynomial ring in $n$ independent variables, where $k$ is a field. In this work we will study Bass numbers of local cohomology modules $H^r_I(R)$ supported on a squarefree monomial ideal $I\subseteq R$. Among them we are mainly interested in Lyubeznik numbers. We build a dictionary between the modules $H^r_I(R)$ and the minimal free resolution of the Alexander dual ideal $I^{\vee }$ that allows us to interpret Lyubeznik numbers as the obstruction to the acyclicity of the linear strands of $I^{\vee }$. The methods we develop also help us to give a bound for the injective dimension of the local cohomology modules in terms of the dimension of the small support.References
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Additional Information
- Josep Àlvarez Montaner
- Affiliation: Department Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Av. Diagonal 647, Barcelona 08028, Spain
- Email: Josep.Alvarez@upc.edu
- Alireza Vahidi
- Affiliation: Department of Mathematics, Payame Noor University, 19395-4697 Tehran, I.R. of Iran
- Email: vahidi.ar@gmail.com
- Received by editor(s): August 14, 2011
- Received by editor(s) in revised form: February 7, 2012, and April 17, 2012
- Published electronically: November 25, 2013
- Additional Notes: The first author was partially supported by MTM2010-20279-C02-01 and SGR2009-1284
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 1829-1855
- MSC (2010): Primary 13D45, 13N10, 13F55
- DOI: https://doi.org/10.1090/S0002-9947-2013-05862-X
- MathSciNet review: 3152714