scholarly journals The Number of Ramified Coverings of the Sphere by the Torus and Surfaces of Higher Genera

2000 ◽  
Vol 4 (1) ◽  
pp. 27-46 ◽  
Author(s):  
I.P. Goulden ◽  
D.M. Jackson ◽  
A. Vainshtein
Keyword(s):  
Ramified Coverings

scholarly journals Convergence of Discrete Period Matrices and Discrete Holomorphic Integrals for Ramified Coverings of the Riemann Sphere

2021 ◽  
Vol 24 (3) ◽  
Author(s):  
Alexander I. Bobenko ◽  
Ulrike Bücking
Keyword(s):  
Error Estimate ◽  
Branch Point ◽  
Riemann Surfaces ◽  
Riemann Sphere ◽  
Holomorphic Functions ◽  
Convergence Result ◽  
Edge Length ◽  
Ramified Covering ◽  
Compact Riemann Surfaces ◽  
Ramified Coverings

AbstractWe consider the class of compact Riemann surfaces which are ramified coverings of the Riemann sphere $\hat {\mathbb {C}}$ ℂ ̂ . Based on a triangulation of this covering we define discrete (multivalued) harmonic and holomorphic functions. We prove that the corresponding discrete period matrices converge to their continuous counterparts. In order to achieve an error estimate, which is linear in the maximal edge length of the triangles, we suitably adapt the triangulations in a neighborhood of every branch point. Finally, we also prove a convergence result for discrete holomorphic integrals for our adapted triangulations of the ramified covering.

Weierstrass multiple points on algebraic curves and ramified coverings

1998 ◽  
Vol 104 (1) ◽  
pp. 335-348 ◽  
Author(s):  
Edoardo Ballico ◽  
Changho Keem
Keyword(s):  
Algebraic Curves ◽  
Multiple Points ◽  
Ramified Coverings

scholarly journals Theorem on the union of two topologically flat cells of codimension 1 inℝn

2006 ◽  
Vol 2006 ◽  
pp. 1-9 ◽  
Author(s):  
A. V. Chernavsky
Keyword(s):  
The Given ◽  
First Time ◽  
Ramified Coverings

In this paper we give a complete and improved proof of the “Theorem on the union of two(n−1)-cells.” First time it was proved by the author in the form of reduction to the earlier author's technique. Then the same reduction by the same method was carried out by Kirby. The proof presented here gives a more clear reduction. We also present here the exposition of this technique in application to the given task. Besides, we use a modification of the method, connected with cyclic ramified coverings, that allows us to bypass referring to the engulfing lemma as well as to other multidimensional results, and so the theorem is proved also for spaces of any dimension. Thus, our exposition is complete and does not require references to other works for the needed technique.

scholarly journals Examples and non-examples of polyhedral Kähler surfaces

2019 ◽  
Vol 70 (3) ◽  
pp. 985-998
Author(s):  
Cécile Gachet
Keyword(s):  
Riemann Surfaces ◽  
The Other ◽  
Two Dimensional ◽  
Complex Surfaces ◽  
Kähler Surfaces ◽  
Ramified Coverings

Abstract Polyhedral Kähler surfaces are a class of complex surfaces, which are flat everywhere except on a two-dimensional skeleton. They are defined as a generalization of the ‘gluing a polygon side by side’ construction of flat Riemann surfaces. In this article, we introduce two classes of polyhedral Kähler surfaces with trivial holonomy: products of polyhedral Kähler curves with zero holonomy and ramified coverings of tori, and prove that none of these classes is contained in the other.

Sign in / Sign up

Export Citation Format

Share Document