Singular factors of rational plane curves

Details Singular factors of rational plane curves Singular factors of rational plane curves

2009-12-14

arxiv.org/abs/0912.2723v3

J. Algebra 357 (2012) 322-346

Mathematics

Commutative Algebra

22 pages, 1 figure, uses pdfsync.sty. Revised version accepted for publication in Journal of Algebra

Scientific paper

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.

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