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 KNIZHNIK-ZAMOLODCHIKOV-BERNARD EQUATIONS ON RIEMANN SURFACES

1995 ◽  
Vol 10 (17) ◽  
pp. 2507-2536 ◽  
Author(s):  
D. IVANOV
Keyword(s):  
Spectral Parameter ◽  
Moduli Space ◽  
Correlation Functions ◽  
Riemann Surfaces ◽  
Projective Structure ◽  
Flat Connection ◽  
Conformal Blocks ◽  
Compact Riemann Surfaces ◽  
Marked Points

Knizhnik-Zamolodchikov-Bernard equations for twisted conformal blocks on compact Riemann surfaces with marked points are written explicitly in a general projective structure in terms of correlation functions in the theory of twisted b−c systems. It is checked that on the moduli space the equations provide a flat connection with the spectral parameter.

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

Compact Riemann Surfaces

2001 ◽  
pp. 161-185
Author(s):  
Raghavan Narasimhan ◽  
Yves Nievergelt
Keyword(s):  
Riemann Surfaces ◽  
Compact Riemann Surfaces
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