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Generalized Samuel Multiplicities of Monomial Ideals and Volumes
Experimental Mathematics ( IF 0.5 ) Pub Date : 2019-11-07 , DOI: 10.1080/10586458.2019.1671919
Rüdiger Achilles 1 , Mirella Manaresi 1
Affiliation  

Abstract

We describe conjecturally the generalized Samuel multiplicities c0,,cd1 of a monomial ideal IK[x1,,xd] in terms of its Newton polyhedron NP(I). More precisely, we conjecture that ci equals the sum of the normalized (di)-volumes of pyramids over the projections of the (di1)-dimensional compact faces of NP(I) along the infinite-directions of i-unbounded facets in which they are contained. For c0 proofs are known (Guibert, Jeffries and Montaño) and for cd1 a proof is given.



中文翻译:

单项理想和体积的广义塞缪尔多重性

摘要

我们推测性地描述了广义的塞缪尔多重性C0,,Cd-1单项式理想ķ[X1,,Xd]就其牛顿多面体而言NP().更准确地说,我们推测c i等于归一化的总和(d-一世)-在投影上的金字塔体积(d-一世-1)维紧致面NP()沿着包含它们的i无界小平面的无限方向。对于c 0的证明是已知的(Guibert、Jeffries 和 Montaño)并且对于Cd-1给出了一个证明。

更新日期:2019-11-07
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