Compact Riemann Surfaces and Algebraic Curves

10.1142/0737 ◽  
1988 ◽  
Author(s):  
Kichoon Yang
Keyword(s):  
Riemann Surfaces ◽  
Algebraic Curves ◽  
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.

A Hodge theoretic projective structure on compact Riemann surfaces

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

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

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.

scholarly journals Isospectral flat connexions

2013 ◽  
Vol 31 (2) ◽  
pp. 279
Author(s):  
S. Srinivas Rau ◽  
Sudhamsh Reddy
Keyword(s):  
Riemann Surfaces ◽  
Higher Rank ◽  
Compact Riemann Surfaces

Isospectral flat connexions are constructed for higher rank bundlesover compact Riemann surfaces

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