A "Staircase" formula for the Chern-Schwartz-MacPherson cycle of a matroid
Combinatorics
2024-11-15 v3 Algebraic Geometry
Abstract
We provide a formula for the Poincar\'e dual of the Chern-Schwartz-MacPherson (CSM) cycle of a matroid in the Chow ring of the matroid. We derive the formula from the case of matroids realizable over the complex numbers and prove that it satisfies a contraction-deletion formula. From this fact, we prove it holds for all matroids, confirming a conjecture of Fife and Rinc\'on.
Keywords
Cite
@article{arxiv.2409.03641,
title = {A "Staircase" formula for the Chern-Schwartz-MacPherson cycle of a matroid},
author = {Franquiz Caraballo Alba and Jeffery Liu},
journal= {arXiv preprint arXiv:2409.03641},
year = {2024}
}