Surfaces of Albanese general type and the Severi conjecture

✍ Scribed by Marco Manetti

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 286 KB
• Volume: 261-262
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310115

✦ Synopsis

Abstract

In 1932, F. Severi claimed, with an incorrect proof, that every smooth minimal projective surface S of irregularity q = q(S) > 0 without irrational pencils of genus q satisfies the topological inequality 2__c__^2^~1~ (S) ≥ c~2~(S).

According to the Enriques‐Kodaira's 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's conjecture. In this paper we prove Severi's conjecture under the additional mild hypothesis that S has ample canonical bundle. Moreover, under the same assumption, we prove that 2__c__^2^~1~ (S) = c~2~(S) if and only if S is a double cover of an abelian surface. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)