Linear systems in $\mathbb{P}^2$ with base points of bounded multiplicity

Abstract

We present a proof of the Harbourne-Hirschowitz conjecture for linear systems with base points of multiplicity seven or less. This proof uses a well-known degeneration of the projective plane, as well as a combinatorial technique that arises from specializing points onto a line.

No major changes. Fixed about a dozen typos and updated journal information