论文标题
品种和切恩·梅瑟类的线性优化
Linear optimization on varieties and Chern-Mather classes
论文作者
论文摘要
线性优化程度给出了在代数模型上优化线性目标函数复杂性的代数衡量。从几何上讲，它可以解释为{offine}综合品种的投影图的程度。我们的第一个结果固定了仿射品种，表明{this} conormal品种的几何形状以多种形式表示，完全决定了给定品种的Chern-Mather类。我们还表明，这些双层与通用仿射切片的线性优化程度一致。
The linear optimization degree gives an algebraic measure of complexity of optimizing a linear objective function over an algebraic model. Geometrically, it can be interpreted as the degree of a projection map on the {affine} conormal variety. Fixing an affine variety, our first result shows that the geometry of {this} conormal variety, expressed in terms of bidegrees, completely determines the Chern-Mather classes of the given variety. We also show that these bidegrees coincide with the linear optimization degrees of generic affine sections.
