  A linear system of plane curves satisfying multiplicity conditions at points
in general position is called special if the dimension is larger than the
expected dimension. A (-1) curve is an irreducible curve with self intersection
-1 and genus zero. The Harbourne-Hirschowitz Conjecture is that a linear system
is special only if a multiple of some fixed (-1) curve is contained in every
curve of the linear system. This conjecture is proven for linear systems with
multiplicity four at all but one of the points.

Algebraic Geometry