Linear Systems of Plane Curves with a Composite Number of Base Points of Equal Multiplicity

Abstract

We extend the range of linear systems of plane curves for which it is known that the dimension is equal to the expected dimension. We use a degeneration technique due to C. Ciliberto and R. Miranda. From our result we deduce, as a Corollary, a theorem due to Evain on homogeneous systems of curves through a number of base points given by a power of 4.