English

The Dimension of Quasi-Homogeneous Linear Systems With Multiplicity Four

Algebraic Geometry 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.math/9905076,
  title  = {The Dimension of Quasi-Homogeneous Linear Systems With Multiplicity Four},
  author = {James Seibert},
  journal= {arXiv preprint arXiv:math/9905076},
  year   = {2007}
}

Comments

21 pages, Latex2e