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

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

2009-01-25

arxiv.org/abs/0901.3889v1

Mathematics

Algebraic Geometry

Scientific paper

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 $\theta$ to two properly intersecting cycles in projective space with the derivatives of the algebraic distance of $\theta$ 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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