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

2015 ◽  
Vol 26 (04) ◽  
pp. 1540003 ◽  
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.

Complete set of Genera of Compact Riemann Surfaces with reference to the point Group of Sulphur (S8) Molecule

2020 ◽  
Vol 32 (7) ◽  
pp. 88-92
Author(s):  
RAFIQUL ISLAM ◽  
◽  
CHANDRA CHUTIA ◽  
Keyword(s):  
Automorphism Group ◽  
Riemann Surfaces ◽  
Point Group ◽  
Finite Point ◽  
Group Of Automorphisms ◽  
Complete Set ◽  
Compact Riemann Surfaces ◽  
Group Of Symmetries

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|

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

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.

scholarly journals ON ODD-DIMENSIONAL COMPLEX ANALYTIC KLEINIAN GROUPS

2019 ◽  
Vol 108 (1) ◽  
pp. 1-32
Author(s):  
MASAHIDE KATO
Keyword(s):  
Group Theory ◽  
Kleinian Group ◽  
Linear Subspace ◽  
Kleinian Groups ◽  
Kähler Manifolds ◽  
Dimensional Case ◽  
Kahler Manifolds ◽  
Discrete Subgroups ◽  
One Dimensional

We shall explain here an idea to generalize classical complex analytic Kleinian group theory to any odd-dimensional cases. For a certain class of discrete subgroups of $\text{PGL}_{2n+1}(\mathbf{C})$ acting on $\mathbf{P}^{2n+1}$, we can define their domains of discontinuity in a canonical manner, regarding an $n$-dimensional projective linear subspace in $\mathbf{P}^{2n+1}$ as a point, like a point in the classical one-dimensional case. Many interesting (compact) non-Kähler manifolds appear systematically as the canonical quotients of the domains. In the last section, we shall give some examples.

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