Canonical heights for abelian group actions of maximal dynamical rank

Hu, Fei  ; Zhong, Guolei 

Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e18

Résumé

Let X be a smooth projective variety of dimension $n\geq 2$ and $G\cong \mathbf {Z}^{n-1}$ a free abelian group of automorphisms of X over $\overline {\mathbf {Q}}$. Suppose that G is of positive entropy. We construct a canonical height function $\widehat {h}_G$ associated with G, corresponding to a nef and big $\mathbf {R}$-divisor, satisfying the Northcott property. By characterizing the zero locus of $\widehat {h}_G$, we prove the Kawaguchi–Silverman conjecture for each element of G. As for other applications, we determine the height counting function for non-periodic points and show that X satisfies potential density.

Détail

DOI : 10.1017/fms.2024.158

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