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

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.

9 pages

Cited by in corpus (1)

• An asymptotic version of Dumnicki's algorithm for linear systems in ${\mathbb{CP}}^2$