A combinatorial proof of non-speciality of systems with at most 9 imposed base points

Marcin Dumnicki


It is known that the Segre-Gimigliano-Harbourne-Hirschowitz Conjecture holds for linear systems of curves with at most 9 imposed base fat points. We give a nice proof based on a combinatorial method of showing non-speciality of such systems. We will also prove, by the same method, that systems $\mathcal L(km;m^{\times k^2})$ and $\mathcal L(km+1;m^{\times k^2})$ are non-special.


linear systems; fat points; Harbourne-Hirschowitz conjecture

Mathematics Subject Classification

14H50; 13P10


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