Diophantine Approximation on Varieties IV: Derivated algebraic distance and derivative metric Bezout Theorem

2009/01/25 by Heinrich Massold, Massold, Heinrich
Mathematics · #11G35 #11G50 #11J13 #14G40 #14J20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G35 #msc:11G50 #msc:11J13 #msc:14G40 #msc:14J20

paper · pdf · doi:10.48550/arxiv.0901.3889

arxiv created 2009/01/25 · arxiv updated 2009/12/01

Abstract

The metric Bezout Theorem proved in an earlier paper can be extended to a derivative version that compares derivatives of the algebraic distance of a point θ to two properly intersecting cycles in projective space with the derivatives of the algebraic distance of θ to their intersection. This improvement can be used to make algebraic independence criteria, to be proved in a forthcoming paper, more flexible and to refine Approximation results that are proved using the metric Bezout Theorem.

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