Double sections, dominating maps, and the Jacobian fibration. (English) Zbl 0967.32015
The authors give two parametrized versions of the uniformization theorem of a nonconstant, nonhyperbolic Riemann surface. The first constructs the uniformization map directly in terms of coordinates via classical complex analysis; the second one, which is coordinate independent, works over any complex curve and is obtained by extending Kodaira’s theory of the Jacobian fibration to a family of singular algebraic curves constructed via algebraic geometry.
Reviewer: Viorel Vâjâitu (Bucureşti)
MSC:
32H02 | Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables |
32S25 | Complex surface and hypersurface singularities |
14H55 | Riemann surfaces; Weierstrass points; gap sequences |
14J17 | Singularities of surfaces or higher-dimensional varieties |