2005/07/12 by Alexander Shapiro, Victor Vinnikov, Shapiro, Alexander +1
Mathematics · #12D10 #14E05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:12D10 #msc:14E05
paper · pdf · doi:10.48550/arxiv.math/0507233
18 pages
arxiv created 2005/07/12 · arxiv updated 2009/12/01
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.