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

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

2005-05-10

arxiv.org/abs/math/0505183v2

Mathematics

Algebraic Geometry

9 pages

Scientific paper

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.

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