Singular factors of rational plane curves
Commutative Algebra
2012-03-20 v3 Algebraic Geometry
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 in [J. Symbolic Comput. 43(2):92-117, 2008]. 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.
Keywords
Cite
@article{arxiv.0912.2723,
title = {Singular factors of rational plane curves},
author = {Laurent Buse and Carlos D'Andrea},
journal= {arXiv preprint arXiv:0912.2723},
year = {2012}
}
Comments
22 pages, 1 figure, uses pdfsync.sty. Revised version accepted for publication in Journal of Algebra