  We study negative curves on surfaces obtained by blowing up special
configurations of points in the complex projective palne. Our main results
concern the following configurations: very general points on a cubic, 3-torsion
points on an elliptic curve and nine Fermat points. As a consequence of our
analysis, we also show that the Bounded Negativity Conjecture holds for the
surfaces we consider. The note contains also some problems for future
attention.
