  We study minimal complex surfaces S of general type with q(S)=q and
p_g(S)=2q-3, q>= 5. We give a complete classification in case that S has a
fibration onto a curve of genus >=2. For these surfaces K^2=8\chi. In general
we prove that K^2>=7\chi-1 and that the stronger inequality K^2\ge 8\chi holds
under extra assumptions (e.g., if the canonical system has no fixed part or the
canonical map has even degree).
  We also describe the Albanese map of S.

Algebraic Geometry