scholarly journals Automorphisms with fixed points and Weierstrass points of compact Riemann surfaces

1993 ◽  
Vol 17 (1) ◽  
pp. 221-249 ◽  
Author(s):  
Katsuaki Yoshida
Keyword(s):  
Fixed Points ◽  
Riemann Surfaces ◽  
Weierstrass Points ◽  
Compact Riemann Surfaces

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.

Weierstrass Points on Compact Riemann Surfaces

1971 ◽  
Vol s2-3 (4) ◽  
pp. 722-724 ◽  
Author(s):  
C. MacLachlan
Keyword(s):  
Riemann Surfaces ◽  
Weierstrass Points ◽  
Compact Riemann Surfaces

scholarly journals On Weierstrass points of non-hyperelliptic compact Riemann surfaces of genus three

1977 ◽  
Vol 7 (3) ◽  
pp. 743-768 ◽  
Author(s):  
Akikazu Kuribayashi ◽  
Kaname Komiya
Keyword(s):  
Riemann Surfaces ◽  
Weierstrass Points ◽  
Compact Riemann Surfaces

On fixed points of involutions of compact Riemann surfaces

2009 ◽  
Vol 105 (1) ◽  
pp. 16 ◽  
Author(s):  
E. Bujalance ◽  
G. Gromadzki ◽  
E. Tyszkowska
Keyword(s):  
Fixed Points ◽  
Riemann Surfaces ◽  
Topological Type ◽  
Teichmüller Space ◽  
Teichmuller Space ◽  
Compact Riemann Surfaces

We find a bound for the total number of fixed points of $k$ commuting involutions of compact Riemann surfaces and we study its attainment. We also find a bound for such number for a pair of non-commuting involutions in terms of the order of their product and the genus of the surface. Finally, we study its attainment, topological type of the action of such pair and the nature of the locus of corresponding surfaces in Teichmüller space.

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.

scholarly journals Weierstrass points on compact Riemann surfaces with nontrivial automorphisms

1981 ◽  
Vol 33 (2) ◽  
pp. 235-246 ◽  
Author(s):  
Nobumasa TAKIGAWA
Keyword(s):  
Riemann Surfaces ◽  
Weierstrass Points ◽  
Compact Riemann Surfaces

scholarly journals ON FIXED POINTS ON COMPACT RIEMANN SURFACES

2011 ◽  
Vol 48 (5) ◽  
pp. 1015-1021
Author(s):  
Grzegorz Gromadzki
Keyword(s):  
Fixed Points ◽  
Riemann Surfaces ◽  
Compact Riemann Surfaces

On Weierstrass Points of a Family of Quartic Curves

2015 ◽  
Vol 25 (14) ◽  
pp. 1540027
Author(s):  
Saleem Mohammed ◽  
Badr Eslam
Keyword(s):  
Finite Group ◽  
Riemann Surfaces ◽  
Group Actions ◽  
Finite Group Actions ◽  
Weierstrass Points ◽  
The Family ◽  
Compact Riemann Surfaces ◽  
Quartic Curves

The aim of this paper is to investigate properties of the Weierstrass points on the family of compact Riemann surfaces [Formula: see text], where [Formula: see text] and [Formula: see text] are parameters such that [Formula: see text] and [Formula: see text] by using finite group actions on this family. Furthermore, the geometry of these points is discussed.

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