De Franchis theorem

In mathematics, the de Franchis theorem is one of a number of closely related statements applying to compact Riemann surfaces, or, more generally, algebraic curves, "X" and "Y", in the case of genus "g" > 1. The simplest is that the automorphism group of "X" is finite (see though Hurwitz's automorphisms theorem). More generally, 
These results are named for (1875–1946). It is sometimes referenced as the De Franchis-Severi theorem. It was used in an important way by Gerd Faltings to prove the Mordell conjecture.