Rational and lacunary algebraic curves

2024/01/10 by Comte, Georges, Tavenas, Sébastien
#14H50 #14Q05 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.05512

Abstract

We give a bound on the number Z of intersection points in a ball of the complex plane, between a rational curve and a lacunary algebraic curve Q=0. This bound depends only on the lacunarity diagram of Q, and in particular is uniform in the coefficients of Q. Our bound shows that Z=O(dm), where d is the degree of Q and m is the number of its monomials.

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