Year: 2009
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Silverman, Joseph H.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W1630558116