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arXiv · 2409.03641

A "Staircase" formula for the Chern-Schwartz-MacPherson cycle of a matroid

Franquiz Caraballo Alba·Jeffery Liu
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Abstract

We provide a formula for the Poincaré 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 Rincón.

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Franquiz Caraballo Alba, Jeffery Liu. 2024-11-14. A "Staircase" formula for the Chern-Schwartz-MacPherson cycle of a matroid. https://arxiv.org/abs/2409.03641

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