Diophantine Approximation on projective Varieties I: Algebraic distance and metric Bézout Theorem

Details Diophantine Approximation on projective Varieties I: Algebraic distance and metric Bézout Theorem Diophantine Approximation on projective Varieties I: Algebraic distance and metric Bézout Theorem

2006-11-23

arxiv.org/abs/math/0611715v2

Mathematics

Number Theory

46 pages

Scientific paper

Apart from the well known algebraic and arithmetic B\'ezout Theorems, there also is the metric B\'ezout 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 $\theta$. Applications of this Theorem will lie in the area of Diophantine Approximation, where one wants to estimate approximation properties of Z with respect to $\theta$ against the ones of X, and Y.

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