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MiS Preprint

Chern-Schwartz-MacPherson cycles of matroids

Lucia Lopez de Medrano, Felipe Rincon and Kristin Shaw


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.

Aug 4, 2017
Aug 11, 2017

Related publications

2020 Repository Open Access
Lucia Lopez de Medrano, Felipe Rincon and Kristin Shaw

Chern-Schwartz-MacPherson cycles of matroids

In: Proceedings of the London Mathematical Society, 120 (2020) 1, pp. 1-27