A Geometric Theory of the Buchsbaum-Rim Multiplicity
A Geometric Theory of the Buchsbaum-Rim Multiplicity
复制标题
Buchsbaum-Rim多重性的几何理论
DOI：
10.1006/jabr.1994.1182
复制
发表时间：
1994
影响因子：
0.9
通讯作者：
A. Thorup
中科院分区：
文献类型：
--
作者：
S. Kleiman;A. Thorup
摘要我们基于初等抽象代数几何发展了一个完备的广义Buchsbaum-Rim重数理论。我们将多重性定义为某些自然交叉数的总和，并根据多项式的前导系数恢复传统的定义，该多项式给出了适当的长度。我们解释的部分和的多重性，在某些密切相关的情况下。我们证明了环中的一个可加性公式，并将不变性与广义的“约化”概念联系起来。“我们建立了一个极多重性公式和一个混合多重性公式，我们确定了四种类型的多重性中的每一种何时消失。最后，我们推广了极大子式的高度不等式和著名的Boger定理。
Abstract We develop a self-contained theory of a generalized Buchsbaum-Rim multiplicity based on elementary abstract algebraic geometry. We define the multiplicity as the sum of certain natural intersection numbers and recover the traditional definition in terms of the leading coefficient of the polynomial that gives the appropriate lengths. We interpret the partial sums as the multiplicities in certain closely associated cases. We prove an additivity formula in the rings and relate constancy to a generalized notion of "reductions." We establish a polar multiplicity formula and a mixed multiplicity formula, and we determine when each of the four types of multiplicities vanish. We end by generalizing the height inequality for maximal minors and a celebrated theorem of Boger.