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$ D$-module structure of local cohomology modules of toric algebras


Author: Jen-Chieh Hsiao
Journal: Trans. Amer. Math. Soc. 364 (2012), 2461-2478
MSC (2010): Primary 13D45, 13N10, 14M25
DOI: https://doi.org/10.1090/S0002-9947-2012-05372-4
Published electronically: January 13, 2012
MathSciNet review: 2888215
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Abstract: Let $ S$ be a toric algebra over a field $ \mathbb{K}$ of characteristic 0 and let $ I$ be a monomial ideal of $ S$. We show that the local cohomology modules $ H^i_I(S)$ are of finite length over the ring of differential operators $ D(S;\mathbb{K})$, generalizing the classical case of a polynomial algebra $ S$. As an application, we compute the characteristic cycles of some local cohomology modules.


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Additional Information

Jen-Chieh Hsiao
Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907
Email: jhsiao@math.purdue.edu

DOI: https://doi.org/10.1090/S0002-9947-2012-05372-4
Received by editor(s): December 17, 2009
Received by editor(s) in revised form: April 8, 2010, and April 14, 2010
Published electronically: January 13, 2012
Additional Notes: The author was partially supported by the NSF under grants DMS 0555319 and DMS 0901123.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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