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Apart from the well known algebraic and arithmetic Bézout Theorems, there also is the metric Bézout Theorem. For two properly intersecting effective cycles in projective space X,Y, and their intersection product Z, it relates not only the degrees and heights of X,Y, and Z, but also their distances and algebraic distances to a given point θ. Applications of this Theorem will lie in the area of Diophantine Approximation, where one wants to estimate approximation properties of Z with respect to θ against the ones of X, and Y. Comments : This is the first of a series of papers by the author. |