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The Dimension of Quasi-Homogeneous Linear Systems With Multiplicity Four

James Seibert
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Abstract

A linear system of plane curves satisfying multiplicity conditions at points in general position is called special if the dimension is larger than the expected dimension. A (-1) curve is an irreducible curve with self intersection -1 and genus zero. The Harbourne-Hirschowitz Conjecture is that a linear system is special only if a multiple of some fixed (-1) curve is contained in every curve of the linear system. This conjecture is proven for linear systems with multiplicity four at all but one of the points.

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James Seibert. 1999-05-12. The Dimension of Quasi-Homogeneous Linear Systems With Multiplicity Four. https://arxiv.org/abs/math/9905076

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