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On the Upper bound of the Multiplicity Conjecture

Tony J. Puthenpurakal
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Abstract

Let $A = K[X_1,...,X_n]$ and let $I$ be a graded ideal in $A$. We show that the upper bound of 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: \begin{enumerate}[\rm (1)] \item radical ideals. \item monomial ideals with generators in different degrees. \item zero-dimensional ideals with generators in different degrees. \end{enumerate} Surprisingly, our proof uses local techniques like analyticity, reductions, equimultiplicity and local results like Rees's theorem on multiplicities.

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Tony J. Puthenpurakal. 2007-10-31. On the Upper bound of the Multiplicity Conjecture. https://arxiv.org/abs/math/0701793

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