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Original Articles

THE DIMENSION OF QUASIHOMOGENEOUS PLANAR LINEAR SYSTEMS WITH MULTIPLICITY FOUR

Pages 1111-1130 | Received 01 Jul 1999, Published online: 20 Aug 2006
 

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 Segre–Harbourne–Hirschowitz Conjecture states that if a linear system is special then 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.

Acknowledgments

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