# Severi type inequalities for irregular surfaces with ample canonical class

### Margarida Mendes Lopes

Instituto Superior Técnico, Lisboa, Portugal### Rita Pardini

Università di Pisa, Italy

## Abstract

Let $S$ be a smooth minimal complex projective surface of maximal Albanese dimension. Under the assumption that the canonical class of $S$ is ample and $q(S):=h^0(\Omega^1_S)\ge 5$, we show

$K^2_S\ge 4\chi(S)+\frac{10}{3}q(S)-8,$

thus improving the well-known Severi inequality $K^2_S\ge 4\chi(S)$.

We also give stronger inequalities under extra assumptions on the Albanese map or on the canonical map of $S$.

## Cite this article

Margarida Mendes Lopes, Rita Pardini, Severi type inequalities for irregular surfaces with ample canonical class. Comment. Math. Helv. 86 (2011), no. 2, pp. 401–414

DOI 10.4171/CMH/228