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TitleOn convolutions of algebraic curves
Author(s) Miroslav Lávička, Jan Vršek
TypeArticle in Journal
AbstractWe focus on the investigation of relations between plane algebraic curves and their convolution. Since the convolution of irreducible algebraic curves is not necessarily irreducible, an upper bound for the number of components is given. Then, a formula expressing the convolution degree using the algebraic degree and the genus of the curve is derived. In addition, a detailed analysis of the so-called special and degenerated components is discussed. We also present some special results for curves with low convolution degree and for rational curves, and use our results to investigate the relation with the theory of the classical offsets and Pythagorean Hodograph (PH) curves presented in Arrondo et al. (1997).
KeywordsAlgebraic curves, Convolutions, Convolution degree, Offsets, Genus, Rational curves
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717110000222
LanguageEnglish
JournalJournal of Symbolic Computation
Volume45
Number6
Pages657 - 676
Year2010
Edition0
Translation No
Refereed No
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