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arXiv · 0908.3835

Height Estimates for Equidimensional Dominant Rational Maps

Joseph H. Silverman
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Abstract

Let F : W --> V be a dominant rational map between quasi-projective varieties of the same dimension. We give two proofs that h_V(F(P)) >> h_W(P) for all points P in a nonempty Zariski open subset of W. For dominant rational maps F : P^n --> P^n, we give a uniform estimate in which the implied constant depends only on n and the degree of F. As an application, we prove a specialization theorem for equidimensional dominant rational maps to semiabelian varieties, providing a complement to Habegger's recent theorem on unlikely intersections.

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Joseph H. Silverman. 2009-08-26. Height Estimates for Equidimensional Dominant Rational Maps. https://arxiv.org/abs/0908.3835

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