A map between Riemann surfaces is holomorphic when its expression in every pair of local complex coordinates is a holomorphic function.
A biholomorphism is a bijective holomorphic map whose inverse is holomorphic. A degree-one nonconstant holomorphic map between compact connected Riemann surfaces is a biholomorphism.
Ancestors (6)
Incoming links (63)
- Affine lift of a holomorphic map between complex tori
- Affine lift of a holomorphic map between one-dimensional complex tori
- Average sheet number
- Biholomorphism
- Double cover of the sphere with four branch values
- Great Picard theorem
- Holomorphic bundle map
- Holomorphic embedding
- Holomorphic map between complex manifolds
- Holomorphic map from the complex plane to a one-dimensional complex torus
- Holomorphic stereographic atlas of the sphere
- Hyperbolic derivative density
- Nonsingular analytic subvariety
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