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.
More generally, These results are named for Michele De Franchis [it] (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.
This algebraic geometry–related article is a stub.