Rational transformations of algebraic curves and elimination theory

Details Rational transformations of algebraic curves and elimination theory Rational transformations of algebraic curves and elimination theory

2005-07-12

arxiv.org/abs/math/0507233v1

Mathematics

Algebraic Geometry

18 pages

Scientific paper

Elimination theory has many applications, in particular, it describes explicitly an image of a complex line under rational transformation and determines the number of common zeroes of two polynomials in one variable. We generalize classical elimination theory and create elimination theory along an algebraic curve using the notion of determinantal representation of algebraic curve. This new theory allows to describe explicitly an image of a plane algebraic curve under rational transformation and to determine the number of common zeroes of two polynomials in two variables on a plane algebraic curve.

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