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- W4298865442 abstract "Let $pi : Eto B$ be an elliptic surface defined over a number field $K$, where $B$ is a smooth projective curve, and let $P: B to E$ be a section defined over $K$ with canonical height $hat{h}_E(P)not=0$. In this article, we show that the function $t mapsto hat{h}_{E_t}(P_t)$ on $B(overline{K})$ is the height induced from an adelically metrized line bundle with non-negative curvature on $B$. Applying theorems of Thuillier and Yuan, we obtain the equidistribution of points $t in B(overline{K})$ where $P_t$ is torsion, and we give an explicit description of the limiting distribution on $B(mathbb{C})$. Finally, combined with results of Masser and Zannier, we show there is a positive lower bound on the height $hat{h}_{A_t}(P_t)$, after excluding finitely many points $t in B$, for any non-special section $P$ of a family of abelian varieties $A to B$ that split as a product of elliptic curves." @default.
- W4298865442 created "2022-10-02" @default.
- W4298865442 creator A5042162519 @default.
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- W4298865442 date "2017-01-27" @default.
- W4298865442 modified "2023-09-25" @default.
- W4298865442 title "Variation of canonical height and equidistribution" @default.
- W4298865442 doi "https://doi.org/10.48550/arxiv.1701.07947" @default.
- W4298865442 hasPublicationYear "2017" @default.
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