Abelian tropical covers
Abstract
Let be a finite abelian group. In this article, we classify harmonic -covers of a tropical curve Γ (which allow dilation along edges and at vertices) in terms of the cohomology group of a suitably defined sheaf on Γ. We give a realizability criterion for harmonic -covers by patching local monodromy data in an extended homology group on Γ. As an explicit example, we work out the case =ℤ/pℤ and explain how realizability for such covers is related to the nowhere-zero flow problem from graph theory.
Citation
Len , Y , Ulirsch , M & Zakharov , D 2023 , ' Abelian tropical covers ' , Mathematical Proceedings of the Cambridge Philosophical Society , vol. FirstView . https://doi.org/10.1017/S0305004123000518
Publication
Mathematical Proceedings of the Cambridge Philosophical Society
Status
Peer reviewed
ISSN
0305-0041Type
Journal article
Description
Funding: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie–Skłodowska–Curie Grant Agreement No. 793039. M.U. has received funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) TRR 326 Geometry and Arithmetic of Uniformized Structures, project number 444845124, by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Sachbeihilfe From Riemann surfaces to tropical curves (and back again), project number 456557832, and from the LOEWE grant Uniformized Structures in Algebra and Geometry. Y.L. has received funding from the EPSRC New Investigator Award (grant number EP/X002004/1).Collections
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