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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Derivations preserving a monomial ideal


Author: Yohannes Tadesse
Journal: Proc. Amer. Math. Soc. 137 (2009), 2935-2942
MSC (2000): Primary 13A15, 13N15, 14Q99
Published electronically: May 4, 2009
MathSciNet review: 2506451
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Abstract: Let $ I$ be a monomial ideal in a polynomial ring $ \mathbf{A}=\mathbf{k}[x_1,\ldots, x_n]$ over a field $ \mathbf{k}$ of characteristic 0, $ T_{\mathbf{A}/\mathbf{k}} (I)$ be the module of $ I$-preserving $ \mathbf{k}$-derivations on $ \mathbf{A}$ and $ G$ be the $ n$-dimensional algebraic torus on $ \mathbf{k}$. We compute the weight spaces of $ T_{\mathbf{A}/\mathbf{k}} (I)$ considered as a representation of $ G$. Using this, we show that $ T_{\mathbf{A}/\mathbf{k}} (I)$ preserves the integral closure of $ I$ and the multiplier ideals of $ I$.


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Additional Information

Yohannes Tadesse
Affiliation: Department of Mathematics, Addis Ababa University, P. O. Box 1176, Addis Ababa, Ethiopia
Address at time of publication: Department of Mathematics, Stockholm University, SE 106-91, Stockholm, Sweden
Email: yohannest@math.aau.edu.et, tadesse@math.su.se

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09922-5
PII: S 0002-9939(09)09922-5
Keywords: Derivations, monomial ideals, multiplier ideals.
Received by editor(s): November 25, 2008
Received by editor(s) in revised form: January 5, 2009
Published electronically: May 4, 2009
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.