Quasi-homogeneous linear systems on $\mathbb P^2$ with base points of multiplicity 7, 8, 9, 10
Tom 100 / 2011
Annales Polonici Mathematici 100 (2011), 277-300 MSC: Primary 14H50; Secondary 14Q05. DOI: 10.4064/ap100-3-5
We prove that the Segre–Gimigliano–Harbourne–Hirschowitz conjecture holds for quasi-homogeneous linear systems on $\mathbb P^2$ for $m=7$, 8, 9, 10, i.e. systems of curves of a given degree passing through points in general position with multiplicities at least $m,\dots,m,m_0$, where $m=7$, 8, 9, 10, $m_0$ is arbitrary.