$D$-module structure of local cohomology modules of toric algebras
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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.References
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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
- 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.
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2888215