{"paper":{"title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS","math.NT"],"primary_cat":"math.AG","authors_text":"Yohsuke Matsuzawa","submitted_at":"2025-07-07T14:10:01Z","abstract_excerpt":"Consider a dominant rational self-map $f$ on a smooth projective variety $X$ defined over $\\overline{\\mathbb{Q}}$. We prove that \\begin{align} \\lim_{n \\to \\infty} \\frac{h_{Y}(f^{n}(x))}{h_{H}(f^{n}(x)) } = 0, \\end{align} where $h_{Y}$ is a height associated with a closed subscheme $Y \\subset X$ of codimension $c$, $h_{H}$ is any ample height on $X$, and $x \\in X(\\overline{\\mathbb{Q}})$ is a point with well-defined orbit, under the following assumptions: (1) either $f$ is a morphism, or $Y$ is pure dimensional, regularly embedded in $X$, and contained in the locus over which all iterates of $f$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05027","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.05027/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}