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Height Estimates for Equidimensional Dominant Rational Maps
- Source :
- J. Ramanujan Math. Soc. 26 (2011), 145--163
- Publication Year :
- 2009
-
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.<br />Comment: 18 pages
Details
- Database :
- arXiv
- Journal :
- J. Ramanujan Math. Soc. 26 (2011), 145--163
- Publication Type :
- Report
- Accession number :
- edsarx.0908.3835
- Document Type :
- Working Paper