A combinatorial proof of non-speciality of systems with at most 9 imposed base points
Abstract
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 L(km; m^(×k²)) and L(km + 1; m^(×k²)) are non-special.
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