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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219657We 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 informationAlgebraic GeometryCommutative Algebra14H50 (Primary) 14N15 (Secondary)Linear systems in $\mathbb{P}^2$ with base points of bounded multiplicitytext