The genus of compact riemann surfaces with maximal automorphism group

In this paper we consider the group of symmetries of the Sulphur molecule (S8 ) which is a finite point group of order 16 denote by D16 generated by two elements having the presentation { u\upsilon/u2= \upsilon8 = (u\upsilon)2 = 1} and find the complete set of genera (g ≥ 2) of Compact Riemann surfaces on which D16 acts as a group of automorphisms as follows: D16 the group of symmetries of the sulphur (S8) molecule of order 16 acts as an automorphism group of a compact Riemann surfaces of genus g ≥ 2 if and only if there are integers \lambda and \mu such that \lambda \leq 1 and \mu \geq 1 and g=\lambda +8\mu (\geq2) , \mu\geq |\lambda|

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Dihedral Groups of Order 2p of Automorphisms of Compact Riemann Surfaces of Genus p – 1

Canadian Mathematical Bulletin ◽

10.4153/cmb-2014-041-3 ◽

2015 ◽

Vol 58 (1) ◽

pp. 196-206

Author(s):

Qingjie Yang ◽

Weiting Zhong

Keyword(s):

Automorphism Group ◽

Conjugacy Class ◽

Riemann Surfaces ◽

Symplectic Group ◽

Dihedral Group ◽

Dihedral Groups ◽

Analytic Automorphism ◽

Compact Riemann Surfaces

AbstractIn this paper we prove that there is only one conjugacy class of dihedral group of order 2p in the 2(p – 1) × 2(p – 1) integral symplectic group that can be realized by an analytic automorphism group of compact connected Riemann surfaces of genus p – 1. A pair of representative generators of the realizable class is also given.

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Stability of pseudoconvexity of disc bundles over compact Riemann surfaces and application to a family of Galois coverings

International Journal of Mathematics ◽

10.1142/s0129167x15400030 ◽

2015 ◽

Vol 26 (04) ◽

pp. 1540003 ◽

Cited By ~ 8

Author(s):

Takeo Ohsawa

Keyword(s):

Automorphism Group ◽

Unit Disc ◽

Riemann Surfaces ◽

Kähler Manifolds ◽

Transformation Groups ◽

Kahler Manifolds ◽

Discrete Subgroups ◽

Stein Manifolds ◽

Galois Coverings ◽

Compact Riemann Surfaces

It is proved that Galois coverings of smooth families of compact Riemann surfaces over Stein manifolds are holomorphically convex if the covering transformation groups are isomorphic to discrete subgroups of the automorphism group of the unit disc. The proof is based on an extension of the fact that disc bundles over compact Kähler manifolds are weakly 1-complete.

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A Hodge theoretic projective structure on compact Riemann surfaces

Journal de Mathématiques Pures et Appliquées ◽

10.1016/j.matpur.2021.02.005 ◽

2021 ◽

Vol 149 ◽

pp. 1-27

Author(s):

Indranil Biswas ◽

Elisabetta Colombo ◽

Paola Frediani ◽

Gian Pietro Pirola

Keyword(s):

Riemann Surfaces ◽

Projective Structure ◽

Compact Riemann Surfaces

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

Mathematical Physics Analysis and Geometry ◽

10.1007/s11040-021-09394-2 ◽

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.

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