Rational transformations of algebraic curves and elimination theory

Abstract

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.

18 pages

Cited by in corpus (5)

• Livsic-type Determinantal Representations and Hyperbolicity
• Several Applications of Bezout Matrices
• Braid Monodromy Type and Rational Transformations of Plane Algebraic Curves
• Elementary Transformations of Pfaffian Representations of Plane Curves
• Rational transformations of systems of commuting nonselfadjoint operators