{"paper":{"title":"Variation of canonical height and equidistribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Laura DeMarco, Niki Myrto Mavraki","submitted_at":"2017-01-27T05:17:53Z","abstract_excerpt":"Let $\\pi : E\\to B$ 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07947","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}