2000/03/31 by Marco Manetti
Mathematics · #math.AG #msc:14J29
published as Math. Nachr. 261-262 (2003) 105-122. · Revised version, with simplified proofs, of an earlier preprint (1997). Latex: 22 pages
arxiv created 2000/12/19 · arxiv updated 2009/11/30
In 1932 F. Severi claimed, with an incorrect proof, that every smooth minimal projective surface S such that the bundle Ω1S is generically generated by global sections satisfies the topological inequality 2c12(S)≥ c2(S). According to Enriques-Kodaira classification, the above inequality is easily verified when the Kodaira dimension of the surface is ≤ 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 2c12(S)=c2(S) if and only if S is a double cover of an abelian surface.