2007/01/27 by Tony J. Puthenpurakal, Puthenpurakal, Tony J. · 1 citation
Computer Science · Mathematics · #13A30 (Secondary) #13D02 (Primary) 13D40 #13H15 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.math/0701793
openalex publication_date 2007/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A = K[X1,...,Xn] 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 Ik and all k ≫ 0) if I belongs to any of the following large classes of ideals: \beginenumerate[\rm (1)] \item radical ideals. \item monomial ideals with generators in different degrees. \item zero-dimensional ideals with generators in different degrees. \endenumerate Surprisingly, our proof uses local techniques like analyticity, reductions, equimultiplicity and local results like Rees's theorem on multiplicities.