On the upper bound of the multiplicity conjecture
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- by Tony J. Puthenpurakal PDF
- Proc. Amer. Math. Soc. 136 (2008), 3429-3434 Request permission
Abstract:
Let $A = K[X_1,\ldots ,X_n]$ and let $I$ be a graded ideal in $A$. We show that the upper bound of the multiplicity conjecture of Herzog, Huneke and Srinivasan holds asymptotically (i.e., for $I^k$ and all $k \gg 0$) if $I$ belongs to any of the following large classes of ideals:
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radical ideals,
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monomial ideals with generators in different degrees,
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zero-dimensional ideals with generators in different degrees.
Surprisingly, our proof uses local techniques like analyticity, reductions, equimultiplicity and local results like Rees’s theorem on multiplicities.
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Additional Information
- Tony J. Puthenpurakal
- Affiliation: Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, India 400 076
- MR Author ID: 715327
- Email: tputhen@math.iitb.ac.in
- Received by editor(s): January 29, 2007
- Received by editor(s) in revised form: September 3, 2007
- Published electronically: May 15, 2008
- Additional Notes: The author thanks the Universtät Duisburg-Essen for its hospitality during November and December of 2006. The author also thanks DFG for financial support, which made this visit possible
- Communicated by: Bernd Ulrich
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3429-3434
- MSC (2000): Primary 13H15, 13D02; Secondary 13D40, 13A30
- DOI: https://doi.org/10.1090/S0002-9939-08-09426-4
- MathSciNet review: 2415026
Dedicated: Dedicated to Juergen Herzog on the occasion of his 65th birthday