Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

On the upper bound of the multiplicity conjecture

Author(s): Tony J. Puthenpurakal
Journal: Proc. Amer. Math. Soc. 136 (2008), 3429-3434.
MSC (2000): Primary 13H15, 13D02; Secondary 13D40, 13A30
Posted: May 15, 2008
MathSciNet review: 2415026
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: Let $A = K[X_1,\ldots,X_n]$ and let be a graded ideal in . We show that the upper bound of the multiplicity conjecture of Herzog, Huneke and Srinivasan holds asymptotically (i.e., for and all $k \gg 0$ ) if 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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