  We study a useful numerical invariant of normal surface singularities,
introduced recently by T. Kawachi. Using this invariant, we give a quick proof
of the (well-known) fact that all log-canonical surface singularities are
either elliptic Gorenstein or rational (without assuming a priori that they are
Q-Gorenstein).
  The main result is a criterion (stated in terms of Kawachi's invariant)
regarding global generation of adjoint linear systems on normal surfaces with
boundary. Such results can be used in proving effective estimates for global
generation on singular threefolds. The theorem of Ein-Lazarsfeld and Kawamata,
which says that the minimal center of log-canonical singularities is always
normal, explains why the results proved here are relevant in that situation.
