On Fixed Points of Conformal Automorphisms of Riemann Surfaces

1988 ◽  
pp. 207-210
Author(s):  
H. Renggli
Keyword(s):  
Fixed Points ◽  
Riemann Surfaces ◽  
Automorphisms Of Riemann Surfaces

scholarly journals Transitive permutation groups with trivial four point stabilizers

2015 ◽  
Vol 18 (5) ◽  
Author(s):  
Kay Magaard ◽  
Rebecca Waldecker
Keyword(s):  
Fixed Points ◽  
Riemann Surfaces ◽  
Permutation Groups ◽  
Weierstrass Points ◽  
Detailed Classification ◽  
Point Stabilizer ◽  
The Relationship ◽  
Automorphisms Of Riemann Surfaces

AbstractIn this paper we analyze the structure of transitive permutation groups that have trivial four point stabilizers, but some nontrivial three point stabilizer. In particular, we give a complete, detailed classification when the group is simple or quasisimple. This paper is motivated by questions concerning the relationship between fixed points of automorphisms of Riemann surfaces and Weierstraß points and is a continuation of the authors' earlier work.

Fixed Points of Automorphisms of Compact Riemann Surfaces

1970 ◽  
Vol 22 (5) ◽  
pp. 922-932 ◽  
Author(s):  
M. J. Moore
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Riemann Surfaces ◽  
Homology Group ◽  
Group Of Automorphisms ◽  
Quartic Curve ◽  
Lefschetz Fixed Point Formula ◽  
Compact Riemann Surfaces ◽  
Klein's Quartic Curve ◽  
Fundamental Paper

In his fundamental paper [3], Hurwitz showed that the order of a group of biholomorphic transformations of a compact Riemann surface S into itself is bounded above by 84(g – 1) when S has genus g ≧ 2. This bound on the group of automorphisms (as we shall call the biholomorphic self-transformations) is attained for Klein's quartic curve of genus 3 [4] and, from this, Macbeath [7] deduced that the Hurwitz bound is attained for infinitely many values of g.After genus 3, the next smallest genus for which the bound is attained is the case g = 7. The equations of such a curve of genus 7 were determined by Macbeath [8] who also gave the equations of the transformations. The equations of these transformations were found by using the Lefschetz fixed point formula. If the number of fixed points of each element of a group of automorphisms is known, then the Lefschetz fixed point formula may be applied to deduce the character of the representation given by the group acting on the first homology group of the surface.

scholarly journals Fixed Points on Asymmetric Riemann Surfaces

2020 ◽  
Vol 17 (4) ◽  
Author(s):  
Ewa Kozłowska-Walania ◽  
Ewa Tyszkowska
Keyword(s):  
Fixed Points ◽  
Riemann Surfaces

Automorphisms of Riemann surfaces

1967 ◽  
Vol 18 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Robert D. M. Accola
Keyword(s):  
Riemann Surfaces ◽  
Automorphisms Of Riemann Surfaces
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