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

 

On the upper bound of the multiplicity conjecture


Author: Tony J. Puthenpurakal
Journal: Proc. Amer. Math. Soc. 136 (2008), 3429-3434
MSC (2000): Primary 13H15, 13D02; Secondary 13D40, 13A30
Published electronically: May 15, 2008
MathSciNet review: 2415026
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Abstract | References | Similar Articles | Additional Information

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:

(1)
radical ideals,
(2)
monomial ideals with generators in different degrees,
(3)
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
Email: tputhen@math.iitb.ac.in

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09426-4
PII: S 0002-9939(08)09426-4
Keywords: Multiplicity conjecture, regularity, reduction, analyticity
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
Dedicated: Dedicated to Juergen Herzog on the occasion of his 65th birthday
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.