Quasi-homogeneous linear systems on P2 with base points of multiplicity 7, 8, 9, 10

Marcin Dumnicki

Quasi-homogeneous linear systems on P2 with base points of multiplicity 7, 8, 9, 10

Algebraic Geometry 2008-04-09 v1 Commutative Algebra

Authors: Marcin Dumnicki

Abstract

In the paper we prove Harbourne-Hirschowitz conjecture for quasi-homogeneous linear systems on $\mathbb P^2$ for $m=7$ , 8, 9, 10, i.e. systems of curves of given degree passing through points in general position with multiplicities at least $m,...,m,m_0$ , where $m=7$ , 8, 9, 10, $m_0$ is arbitrary.

Keywords

Harbourne-Hirschowitz conjecture quasi-homogeneous linear systems projective plane base points multiplicity algebraic geometry curves

Cite

@article{arxiv.0804.1213,
  title  = {Quasi-homogeneous linear systems on P2 with base points of multiplicity 7, 8, 9, 10},
  author = {Marcin Dumnicki},
  journal= {arXiv preprint arXiv:0804.1213},
  year   = {2008}
}

Comments

13 pages

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