论文标题
Matroid Chern-Schwartz-Macpherson周期和Tutte活动
Matroid Chern-Schwartz-MacPherson cycles and Tutte activities
论文作者
论文摘要
Lopéz de Medrano-Rinćon-Shaw defined Chern-Schwartz-MacPherson cycles for an arbitrary matroid $M$ and proved by an inductive geometric argument that the unsigned degrees of these cycles agree with the coefficients of $T(M;x,0)$, where $T(M;x,y)$ is the Tutte polynomial associated to $M$. Ardila-Denham-Huh最近利用了对这些系数的这种解释，以证明其对数洞穴。在本说明中，我们通过将其稳定的相交与适当的编码的通用热带线性空间进行稳定的相交，并表明加权点数量与Gioan-Las Vergn的精制活动相吻合，从而直接计算了Matroid Chern-Schwartz-Macpherson循环的程度。
Lopéz de Medrano-Rinćon-Shaw defined Chern-Schwartz-MacPherson cycles for an arbitrary matroid $M$ and proved by an inductive geometric argument that the unsigned degrees of these cycles agree with the coefficients of $T(M;x,0)$, where $T(M;x,y)$ is the Tutte polynomial associated to $M$. Ardila-Denham-Huh recently utilized this interpretation of these coefficients in order to demonstrate their log-concavity. In this note we provide a direct calculation of the degree of a matroid Chern-Schwartz-MacPherson cycle by taking its stable intersection with a generic tropical linear space of the appropriate codimension and showing that the weighted point count agrees with the Gioan-Las Vergnas refined activities expansion of the Tutte polynomial.
