Chern-Schwartz-MacPherson cycles of matroids
Lucia Lopez de Medrano, Felipe Rincon, and Kristin Shaw
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Submission date: 04. Aug. 2017
published in: Proceedings of the London Mathematical Society, 120 (2020) 1, p. 1-27
DOI number (of the published article): 10.1112/plms.12278
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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.