Chern-Schwartz-MacPherson cycles of matroids
Combinatorics
2019-08-14 v1 Algebraic Geometry
Abstract
We define Chern-Schwartz-MacPherson (CSM) cycles of an arbitrary matroid. These are balanced weighted fans supported on the skeleta of the corresponding Bergman fan. In the case that the matroid arises from a complex hyperplane arrangement A, we show that these cycles represent the CSM class of the complement of A. We also prove that for any matroid, the degrees of its CSM cycles are given by the coefficients of (a shift of) the reduced characteristic polynomial, and that CSM cycles are valuations under matroid polytope subdivisions.
Keywords
Cite
@article{arxiv.1707.07303,
title = {Chern-Schwartz-MacPherson cycles of matroids},
author = {Lucia Lopez de Medrano and Felipe Rincon and Kristin Shaw},
journal= {arXiv preprint arXiv:1707.07303},
year = {2019}
}
Comments
26 pages