New effective bounds on the dimension of a linear system in $\mathbb P^2$

Marcin Dumnicki; Witold Jarnicki

New effective bounds on the dimension of a linear system in $\mathbb P^2$

Algebraic Geometry 2016-09-07 v2

Authors: Marcin Dumnicki , Witold Jarnicki

Abstract

The main goal of this paper is to present an algorithm bounding the dimension of a linear system of curves of given degree (or monomial basis) with multiple points in general position. As a result we prove the Hirschowitz--Harbourne Conjecture when the multiplicities of base points are bounded by 11.

Keywords

linear systems curves multiple points general position hirschowitz-harbourne conjecture effective bounds

Cite

@article{arxiv.math/0505183,
  title  = {New effective bounds on the dimension of a linear system in $\mathbb P^2$},
  author = {Marcin Dumnicki and Witold Jarnicki},
  journal= {arXiv preprint arXiv:math/0505183},
  year   = {2016}
}

Comments

9 pages

Related papers

View all related →