A "Staircase" formula for the Chern-Schwartz-MacPherson cycle of a matroid
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912118171762688 |
|---|---|
| author | Alba, Franquiz Caraballo Liu, Jeffery |
| author_facet | Alba, Franquiz Caraballo Liu, Jeffery |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03641 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A "Staircase" formula for the Chern-Schwartz-MacPherson cycle of a matroid Alba, Franquiz Caraballo Liu, Jeffery Combinatorics Algebraic Geometry 14C17 (Primary) 14N20, 05B35 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. |
| title | A "Staircase" formula for the Chern-Schwartz-MacPherson cycle of a matroid |
| topic | Combinatorics Algebraic Geometry 14C17 (Primary) 14N20, 05B35 |
| url | https://arxiv.org/abs/2409.03641 |