scholarly journals On automorphism groups of compact Riemann surfaces with prescribed group structure

1991 ◽  
Vol 67 (2) ◽  
pp. 43-44 ◽  
Author(s):  
Hideyuki Kimura
Keyword(s):  
Riemann Surfaces ◽  
Automorphism Groups ◽  
Group Structure ◽  
Compact Riemann Surfaces

scholarly journals Weierstrass points on modular curves X0(N) fixed by the Atkin–Lehner involutions

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mustafa Bojakli ◽  
Hasan Sankari
Keyword(s):  
Riemann Surfaces ◽  
Coding Theory ◽  
Design Methodology ◽  
Automorphism Groups ◽  
Group Structure ◽  
Weierstrass Point ◽  
Algebraic Number Theory ◽  
Content Type ◽  
Weierstrass Points ◽  
Compact Riemann Surfaces

PurposeThe authors have determined whether the points fixed by all the full and the partial Atkin–Lehner involutions WQ on X0(N) for N ≤ 50 are Weierstrass points or not.Design/methodology/approachThe design is by using Lawittes's and Schoeneberg's theorems.FindingsFinding all Weierstrass points on X0(N) fixed by some Atkin–Lehner involutions. Besides, the authors have listed them in a table.Originality/valueThe Weierstrass points have played an important role in algebra. For example, in algebraic number theory, they have been used by Schwartz and Hurwitz to determine the group structure of the automorphism groups of compact Riemann surfaces of genus g ≥ 2. Whereas in algebraic geometric coding theory, if one knows a Weierstrass nongap sequence of a Weierstrass point, then one is able to estimate parameters of codes in a concrete way. Finally, the set of Weierstrass points is useful in studying arithmetic and geometric properties of X0(N).

scholarly journals Automorphism groups of compact Riemann surfaces of genera three and four

1990 ◽  
Vol 65 (3) ◽  
pp. 277-292 ◽  
Author(s):  
Izumi Kuribayashi ◽  
Akikazu Kuribayashi
Keyword(s):  
Riemann Surfaces ◽  
Automorphism Groups ◽  
Compact Riemann Surfaces

scholarly journals Automorphism groups of compact riemann surfaces of genus five

1990 ◽  
Vol 134 (1) ◽  
pp. 80-103 ◽  
Author(s):  
Akikazu Kuribayashi ◽  
Hideyuki Kimura
Keyword(s):  
Riemann Surfaces ◽  
Automorphism Groups ◽  
Compact Riemann Surfaces

scholarly journals Automorphism groups, isomorphic to ${\rm GL}(3,{\bf F}_2)$, of compact Riemann surfaces

1991 ◽  
Vol 43 (3) ◽  
pp. 337-353 ◽  
Author(s):  
Akikazu Kuribayashi ◽  
Hideyuki Kimura
Keyword(s):  
Riemann Surfaces ◽  
Automorphism Groups ◽  
Compact Riemann Surfaces

scholarly journals Automorphism Groups of Symmetric and Pseudo-real Riemann Surfaces

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Ewa Tyszkowska
Keyword(s):  
Riemann Surfaces ◽  
Algebraic Curve ◽  
Algebraic Curves ◽  
Automorphism Groups ◽  
Real Riemann Surfaces ◽  
Compact Riemann Surfaces

AbstractThe category of smooth, irreducible, projective, complex algebraic curves is equivalent to the category of compact Riemann surfaces. We study automorphism groups of Riemann surfaces which are equivalent to complex algebraic curves with real moduli. A complex algebraic curve C has real moduli when the corresponding surface $$X_C$$ X C admits an anti-conformal automorphism. If no such an automorphism is an involution (symmetry), then the surface $$X_C$$ X C is called pseudo-real and the curve C is isomorphic to its conjugate, but is not definable over reals. Otherwise, the surface $$X_C$$ X C is called symmetric and the curve C is real.

scholarly journals A note on large automorphism groups of compact Riemann surfaces

2020 ◽  
Vol 547 ◽  
pp. 1-21 ◽  
Author(s):  
Milagros Izquierdo ◽  
Sebastián Reyes-Carocca
Keyword(s):  
Riemann Surfaces ◽  
Automorphism Groups ◽  
Compact Riemann Surfaces
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