English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
 
 
DownloadE-Mail
  Riemann surfaces of second kind and effective finiteness theorems

Jöricke, B. (2022). Riemann surfaces of second kind and effective finiteness theorems. Mathematische Zeitschrift, 302(1), 73-127. doi:10.1007/s00209-022-03018-3.

Item is

Files

show Files
hide Files
:
Jöricke_Riemann surfaces of second kind and effective finiteness theorems_2022.pdf (Publisher version), 2MB
Name:
Jöricke_Riemann surfaces of second kind and effective finiteness theorems_2022.pdf
Description:
-
OA-Status:
Hybrid
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
Technical Metadata:
Copyright Date:
-
Copyright Info:
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License:
-
:
2102.02139.pdf (Preprint), 2MB
Name:
2102.02139.pdf
Description:
-
OA-Status:
Green
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
Technical Metadata:
Copyright Date:
-
Copyright Info:
-

Locators

show
hide
Locator:
https://doi.org/10.1007/s00209-022-03018-3 (Publisher version)
Description:
-
OA-Status:
Hybrid
Description:
-
OA-Status:
Green

Creators

show
hide
 Creators:
Jöricke, Burglind1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

Content

show
hide
Free keywords: Mathematics, Complex Variables
 Abstract: The Geometric Shafarevich Conjecture and the Theorem of de Franchis state the
finiteness of the number of certain holomorphic objects on closed or punctured
Riemann surfaces. The analog of these kind of theorems for Riemann surfaces of
second kind is an estimate of the number of irreducible holomorphic objects up
to homotopy (or isotopy, respectively). This analog can be interpreted as a
quantitatve statement on the limitation for Gromov's Oka principle.
For any finite open Riemann surface $X$ (maybe, of second kind) we give an
effective upper bound for the number of irreducible holomorphic mappings up to
homotopy from $X$ to the twice punctured complex plane, and an effective upper
bound for the number of irreducible holomorphic torus bundles up to isotopy on
such a Riemann surface. The bound depends on a conformal invariant of the
Riemann surface.
If $X_{\sigma}$ is the $\sigma$-neighbourhood of a skeleton of an open
Riemann surface with finitely generated fundamental group, then the number of
irreducible holomorphic mappings up to homotopy from $X_{\sigma}$ to the twice
punctured complex plane grows exponentially in $\frac{1}{\sigma}$.

Details

show
hide
Language(s): eng - English
 Dates: 2022
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 2102.02139
DOI: 10.1007/s00209-022-03018-3
 Degree: -

Event

show

Legal Case

show

Project information

show

Source 1

show
hide
Title: Mathematische Zeitschrift
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: Springer
Pages: - Volume / Issue: 302 (1) Sequence Number: - Start / End Page: 73 - 127 Identifier: -