  In this paper we collect some results on the obstruction spaces for rational
surface singularities and minimally elliptic surface singularities. Based on
the known results we calculate higher obstruction spaces for such surface
singularities. The results imply that in general the higher obstruction spaces
of deforming semi-log-canonical surfaces do not vanish. We apply the
calculation result to show that there is no Li-Tian and Behrend-Fantechi style
virtual fundamental class on such moduli space of semi-log-canonical surfaces.
