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Article overview
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Chern Classes of Tropical Manifolds | | Lucía López de Medrano
; Felipe Rincón
; Kris Shaw
; | | Date: |
1 Sep 2023 | | Abstract: | We extend the definitions of Chern-Schwartz-MacPherson (CSM) cycles of
matroids to tropical manifolds. To do this, we provide an alternate description
of CSM cycles of matroids which is invariant under integer affine
transformations. Utilising results of Esterov and Katz-Stapledon, we prove
correspondence theorems for the CSM classes of tropicalisations of subvarieties
of toric varieties. We also provide an adjunction formula relating the CSM
cycles of a tropical manifold and a codimension-one tropical submanifold.
Lastly, we establish Noether’s Formula for compact tropical surfaces with a
Delzant face structure. This extends the class of surfaces for which the
formula had been previously proved by the third author. | | Source: | arXiv, 2309.00229 | | Services: | Forum | Review | PDF | Favorites | |
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