Linear systems over $\mathbb P^1\times\mathbb P^1$ with base points of multiplicity bounded by three

Volume 101 / 2011

Tomasz Lenarcik Annales Polonici Mathematici 101 (2011), 105-122 MSC: Primary 14H50; Secondary 14Q05. DOI: 10.4064/ap101-2-1


We propose a combinatorial method of proving non-specialty of a linear system of curves with multiple points in general position. As an application, we obtain a classification of special linear systems on ${\mathbb P}^1\times{\mathbb P}^1$ with multiplicities not exceeding $3$.


  • Tomasz LenarcikInstitute of Mathematics
    Jagiellonian University
    30-348 Kraków, Poland

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