New effective bounds on the dimension of a linear system in \(\mathbb P^2\) (Q2455749)
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| English | New effective bounds on the dimension of a linear system in \(\mathbb P^2\) |
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New effective bounds on the dimension of a linear system in \(\mathbb P^2\) (English)
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26 October 2007
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The authors use formal computational methods (Gröbner bases) to check the Harbourne-Hirschowitz conjecture on linear systems of plane curves with fixed multiplicities at general points in several cases (e.g. for multiplicities \(\leq 11\)). In the meantime more general results appeared (e.g. multiplicities \(\leq 20\) in \textit{S. Yang} [J. Algebr. Geom. 16, No. 1, 19--38 (2007; Zbl 1115.14003)]).
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Harbourne-Hirschowitz conjecture
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plane curves with prescribed multiplicities
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