On the upper bound of the multiplicity conjecture

Puthenpurakal, Tony

doi:10.1090/S0002-9939-08-09426-4

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:

radical ideals,
monomial ideals with generators in different degrees,
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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