JournalscmhVol. 86, No. 2pp. 401–414

Severi type inequalities for irregular surfaces with ample canonical class

  • Margarida Mendes Lopes

    Instituto Superior Técnico, Lisboa, Portugal
  • Rita Pardini

    Università di Pisa, Italy
Severi type inequalities for irregular surfaces with ample canonical class cover
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Abstract

Let SS be a smooth minimal complex projective surface of maximal Albanese dimension. Under the assumption that the canonical class of SS is ample and q(S):=h0(ΩS1)5q(S):=h^0(\Omega^1_S)\ge 5, we show

KS24χ(S)+103q(S)8,K^2_S\ge 4\chi(S)+\frac{10}{3}q(S)-8,

thus improving the well-known Severi inequality KS24χ(S)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 SS.

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