Double sections, dominating maps, and the Jacobian fibration. (English) Zbl 0967.32015

Buzzard, Gregery T.; Lu, Steven S.-Y.

Am. J. Math. 122, No. 5, 1061-1084 (2000).

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

Keywords:

double section; dominating map; Riemann surface; uniformization map; Jacobian fibration