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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
49/2017

Chern-Schwartz-MacPherson cycles of matroids

Lucia Lopez de Medrano, Felipe Rincon and Kristin Shaw

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.

Received:
Aug 4, 2017
Published:
Aug 11, 2017

Related publications

inJournal
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