Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Algebraic Geometry

arXiv:2201.04385 (math)
[Submitted on 12 Jan 2022]

Title:Riemann-Hurwitz theorem and second main theorem for harmonic morphisms on graphs or metrized complexes

Authors:Tingbin Cao, Mengnan Cheng
View PDF
Abstract:In this article, we mainly obtain the Riemann-Hurwitz theorems for harmonic morphisms on (vertex-weighted) metric graphs or metrized complexes of algebraic curves, inspired of the recent work on harmonic morphisms of graphs or metrized complexes due to many researchers. By making use of these Riemann-Hurwitz theorems, we then systematically establish the second main theorems for harmonic morphisms on finite graphs, vertex-weighted graphs, (vertex-weighted) metric graphs or metrized complexes of algebraic curves, from the viewpoint of Nevanlinna theory.
Comments: 36 pages
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14N10, 05E14, 05C10, 30D35
Cite as: arXiv:2201.04385 [math.AG]
  (or arXiv:2201.04385v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.2201.04385

Submission history

From: Tingbin Cao [view email]
[v1] Wed, 12 Jan 2022 09:44:17 UTC (535 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.AG
< prev   |   next >
new | recent | 2022-01
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)