2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226073Let 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 HelveticiAlgebraic Geometry14J29text