An upper bound for the height for regular affine automorphisms of A^n

Details An upper bound for the height for regular affine automorphisms of A^n An upper bound for the height for regular affine automorphisms of A^n

2009-09-16

arxiv.org/abs/0909.3107v1

Mathematics

Number Theory

Scientific paper

In 2006, Kawaguchi proved a lower bound for height of h(f(P)) when f is a regular affine automorphism of A^2, and he conjectured that a similar estimate is also true for regular affine automorphisms of A^n for n>2. In this paper we prove Kawaguchi's conjecture. This implies that Kawaguchi's theory of canonical heights for regular affine automorphisms of projective space is true in all dimensions.

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