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