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

Marcin Dumnicki; Witold Jarnicki

arxiv: math/0505183 · v2 · pith:EB4RHPZOnew · submitted 2005-05-10 · 🧮 math.AG

New effective bounds on the dimension of a linear system in mathbb P²

Marcin Dumnicki , Witold Jarnicki This is my paper

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keywords dimensionlinearpointssystemalgorithmbasebasisbounded

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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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New effective bounds on the dimension of a linear system in mathbb P²

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