An Abel–Jacobi theorem for metrized complexes of Riemann surfaces
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Maximilian C. E. Hofmann
Abstract
Motivated by the recent surge of interest in the geometry of hybrid spaces, we prove an Abel–Jacobi theorem for a metrized complex of Riemann surfaces, generalizing both the classical Abel–Jacobi theorem and its tropical analogue.
Funding statement: This project has received funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) TRR 326 Geometry and Arithmetic of Uniformized Structures, project number 444845124, from the DFG Sachbeihilfe FromRiemann surfaces to tropical curves (and back again), project number 456557832, as well as the DFG Sachbeihilfe Rethinking tropical linear algebra: Buildings, bimatroids, and applications, project number 539867663, within the SPP 2458 Combinatorial Synergies.
Acknowledgements
The authors would like to thank Andreas Gross for helpful discussions en route to this article. Remarks from the anonymous referee have significantly improved the structure of our main argument and, for example, also led to a simpler proof of Proposition 3.1. We thank the referee for generously sharing their ideas.
Communicated by: R. Cavalieri
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Articles in the same Issue
- Frontmatter
- Polyhedral combinatorics of bisectors
- Explicit construction of decomposable Jacobians
- Some rigidity results on q-solitons
- Quasimorphisms on nonorientable surface diffeomorphism groups
- On nearly optimal paper Moebius bands
- Desargues’ Theorem in Laguerre Planes
- Simple obstructions and cone reduction
- The Bogomolov–Gieseker–Koseki inequality on surfaces with canonical singularities in arbitrary characteristic
- The simultaneous lattice packing-covering constant of octahedra
- An Abel–Jacobi theorem for metrized complexes of Riemann surfaces
- Exploring the interplay of semistable vector bundles and their restrictions on reducible curves
- Another proof of Segre’s theorem about ovals
Articles in the same Issue
- Frontmatter
- Polyhedral combinatorics of bisectors
- Explicit construction of decomposable Jacobians
- Some rigidity results on q-solitons
- Quasimorphisms on nonorientable surface diffeomorphism groups
- On nearly optimal paper Moebius bands
- Desargues’ Theorem in Laguerre Planes
- Simple obstructions and cone reduction
- The Bogomolov–Gieseker–Koseki inequality on surfaces with canonical singularities in arbitrary characteristic
- The simultaneous lattice packing-covering constant of octahedra
- An Abel–Jacobi theorem for metrized complexes of Riemann surfaces
- Exploring the interplay of semistable vector bundles and their restrictions on reducible curves
- Another proof of Segre’s theorem about ovals
