Abstract
Fixing n general points pi in the plane, what is the dimension of the space of plane curves of degree d having multiplicity mi at pi for each i? In this article we propose an approach to attack this problem, and demonstrate it by successfully computing this dimension for all n and for mi constant, at most 3. This application, while previously known (see (Hi1)), demonstrates the utility of our approach, which is based on an analysis of the corresponding linear system on a degeneration of the plane itself, leading to a simple recursion for these dimensions. We also obtain results in the quasi-homogeneous case when all the multiplicities are equal except one; this is the natural family to consider in the recursion.
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