科研之友
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摘要
Let phi : W -> V be a dominant rational map between quasi-projective varieties of the same dimension. We give two proofs that h(V) (phi (P)) >> h(W) (P) for all points P in a nonempty Zariski open subset of W. For dominant rational maps phi : P-n -> Pn, we give a uniform estimate in which the implied constant depends only on n and the degree of-phi. 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.
- 出版日期2011-6
