An orbifold approach to Severi Inequality

Abstract

For a smooth minimal surface of general type $S$ with $Albdim(S)=2$, Severi inequality says that $K_S^2\ge 4\chi (S)$, which was proved by Pardini. It is expected that when the equality is attained, $S$ is birational to a double cover over an Abelian surface branched along a divisor having at most negligible singularities. This was proved when $K_S$ is ample by Manetti. In this paper, we applied Manetti's method to the canonical model of $S$, with some additional assumptions we proved Severi inequality and characterized the surfaces with $K_S^2=4\chi (S)$.In addition, we gave a characterization of the double cover over an Abelian surface via the ramification divisor.

This paper has been withdrawn, because Severi problem has been solved completely by Rita Pardini,Xin Lv et

References in corpus (1)

• Severi type inequalities for irregular surfaces with ample canonical class

Cited by in corpus (1)

• Generalized Clifford-Severi Inequality and the Volume of Irregular Varieties