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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
中文翻译:
单项理想和体积的广义塞缪尔多重性
更新日期:2019-11-07
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 of a monomial ideal in terms of its Newton polyhedron More precisely, we conjecture that ci equals the sum of the normalized -volumes of pyramids over the projections of the -dimensional compact faces of along the infinite-directions of i-unbounded facets in which they are contained. For c0 proofs are known (Guibert, Jeffries and Montaño) and for 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单项式理想就其牛顿多面体而言更准确地说,我们推测c i等于归一化的总和-在投影上的金字塔体积维紧致面沿着包含它们的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)并且对于给出了一个证明。