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An upper bound for the height for regular affine automorphisms of \({{{\mathbb{A}}^ n}}\)

A height bound for regular affine automorphisms

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Abstract

Kawaguchi (Math. Ann. 335(2):285–310, 359–374, 2006) proved a height inequality for \({h\bigl(f(P)\bigr)}\) when f is a regular affine automorphism of \({{\mathbb{A}}^2}\) , and he conjectured that a similar estimate is also true for regular affine automorphisms of \({{\mathbb{A}}^n}\) for n ≥ 3. 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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  1. Department of Mathematics, University of Illinois at Chicago, Chicago, IL, 60607, USA

    Chong Gyu Lee

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  1. Chong Gyu Lee
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Correspondence to Chong Gyu Lee.

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Lee, C.G. An upper bound for the height for regular affine automorphisms of \({{{\mathbb{A}}^ n}}\) . Math. Ann. 355, 1–16 (2013). https://doi.org/10.1007/s00208-011-0775-8

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  • DOI: https://doi.org/10.1007/s00208-011-0775-8

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