Uniformly effective Shafarevich Conjecture on families of hyperbolic curves over a curve with prescribed degeneracy locus

Details Uniformly effective Shafarevich Conjecture on families of hyperbolic curves over a curve with prescribed degeneracy locus Uniformly effective Shafarevich Conjecture on families of hyperbolic curves over a curve with prescribed degeneracy locus

2003-11-06

arxiv.org/abs/math/0311085v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

The paper's main result is an effective uniform bound for the finiteness statement of the Shafarevich Conjecture over function fields. Several results on the projective geometry of curves are established in the course of the proof. These results should be of independent interest. As a corollary, a uniform effective bound for the Mordell Conjecture over function fields is derived via Parshin's trick.

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