论文标题
代数多重性的新分析和几何方面
New Analytical and Geometrical Aspects of the Algebraic Multiplicity
论文作者
论文摘要
本文揭示了[7，5]中引入的广义代数多样性的一些新的分析和几何特性，即$χ$，并在[20，23，24]中进一步开发。特别是，它在$χ$和代数变种的局部交叉点索引概念之间建立了一个全新的联系，这是代数几何的中心设备。非线性光谱理论与代数几何形状之间的这种联系为$χ$提供了深刻的几何含义。此外，$χ$是通过与线性路径相关的Schur操作员的新概念来表征的。
This paper reveals some new analytical and geometrical properties of the generalized algebraic multiplicity, $χ$, introduced in [7, 5] and further developed in [20, 23, 24]. In particular, it establishes a completely new connection between $χ$ and the concept of local intersection index of algebraic varieties, a central device in Algebraic Geometry. This link between Nonlinear Spectral Theory and Algebraic Geometry provides to $χ$ with a deep geometrical meaning. Moreover, $χ$ is characterized through the new notion of local determinant of the Schur operator associated to the linear path, $\mathfrak{L}(λ)$.
