Severi type inequalities for irregular surfaces with ample canonical class
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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>= 4χ(S)+(10/3)q(S)-8, thus improving the well known Severi inequality K^2>=4χ(S). We also give stronger inequalities under extra assumptions on the Albanese map or on the canonical map of S.
13 pp., to apear in Commentarii Mathematici Helvetici
13 pp., to apear in Commentarii Mathematici Helvetici