  In 1932 F. Severi claimed, with an incorrect proof, that every smooth minimal
projective surface $S$ such that the bundle $\Omega^1_S$ is generically
generated by global sections satisfies the topological inequality $2c_1^2(S)\ge
c_2(S)$. According to Enriques-Kodaira classification, the above inequality is
easily verified when the Kodaira dimension of the surface is $\le 1$, while for
surfaces of general type it is still an open problem known as Severi
conjecture. In this paper we prove Severi conjecture under the additional mild
hypothesis that $S$ has ample canonical bundle. Moreover, under the same
assumption, we prove that $2c_1^2(S)=c_2(S)$ if and only if $S$ is a double
cover of an abelian surface.
