Commentarii Mathematici Helvetici


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Volume 86, Issue 2, 2011, pp. 401–414
DOI: 10.4171/CMH/228

Published online: 2011-02-27

Severi type inequalities for irregular surfaces with ample canonical class

Margarida Mendes Lopes[1] and Rita Pardini[2]

(1) Instituto Superior Técnico, Lisboa, Portugal
(2) Università di Pisa, Italy

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 $S$.

Keywords: Surfaces of general type, irregular surfaces, cotangent bundle, cotangent map, Albanese map, numerical invariants

Mendes Lopes Margarida, Pardini Rita: Severi type inequalities for irregular surfaces with ample canonical class. Comment. Math. Helv. 86 (2011), 401-414. doi: 10.4171/CMH/228