Severi type inequalities for irregular surfaces with ample canonical class

Details Severi type inequalities for irregular surfaces with ample canonical class Severi type inequalities for irregular surfaces with ample canonical class

2009-04-06

arxiv.org/abs/0904.1004v1

Mathematics

Algebraic Geometry

13 pp., to apear in Commentarii Mathematici Helvetici

Scientific paper

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 the irregularity of S, q(S), is greater or equal to 5 we show that K^2>= 4\chi(S)+(10/3)q(S)-8, thus improving the well known Severi inequality K^2>=4\chi(S). We also give stronger inequalities under extra assumptions on the Albanese map or on the canonical map of S.

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