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TitleNew effective bounds on the dimension of a linear system in
Author(s) Marcin Dumnicki, Witold Jarnicki
TypeArticle in Journal
AbstractThe main goal of this paper is to present an algorithm bounding the dimension of a linear system of plane curves of given degree (or monomial basis) with multiple points in general position. As a result we prove the Harbourne–Hirschowitz conjecture when the multiplicities of base points are bounded by 11. This gives a partial answer to the question of when bivariate polynomial interpolation is possible.
KeywordsHarbourne–Hirschowitz conjecture, Zero-dimensional schemes, Gröbner bases
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717107000120
LanguageEnglish
JournalJournal of Symbolic Computation
Volume42
Number6
Pages621 - 635
Year2007
Edition0
Translation No
Refereed No
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