THE DIMENSION OF QUASIHOMOGENEOUS PLANAR LINEAR SYSTEMS WITH MULTIPLICITY FOUR

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.

Keywords:

• Algebraic Geometry
• Linear systems
• Hermite interpolation
• Plane curves

Acknowledgments