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Singular factors of rational plane curves

Laurent Busé 1 Carlos d'Andrea 2 
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (1965 - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We give a complete factorization of the invariant factors of resultant matrices built from birational parameterizations of rational plane curves in terms of the singular points of the curve and their multiplicity graph. This allows us to prove the validity of some conjectures about these invariants stated by Chen, Wang and Liu. As a byproduct, we also give a complete factorization of the D-resultant for rational functions in terms of the similar data extracted from the multiplicities.
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Submitted on : Wednesday, July 4, 2012 - 10:56:33 PM
Last modification on : Thursday, August 4, 2022 - 4:52:36 PM
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Laurent Busé, Carlos d'Andrea. Singular factors of rational plane curves. Journal of Algebra, 2012, 357, pp.322-346. ⟨hal-00714544⟩



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