{"paper":{"title":"Polynomial log-volume growth in slow dynamics and the GK-dimensions of twisted homogeneous coordinate rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.RA"],"primary_cat":"math.AG","authors_text":"De-Qi Zhang, Hsueh-Yung Lin, Keiji Oguiso","submitted_at":"2021-04-07T22:44:13Z","abstract_excerpt":"Let f be a zero entropy automorphism of a compact K\\\"ahler manifold X. We study the polynomial log-volume growth Plov(f) of f in light of the dynamical filtrations introduced in our previous work with T.-C. Dinh. We obtain new upper bounds and lower bounds of Plov(f). As a corollary, we completely determine Plov(f) when dim X = 3, extending a result of Artin--Van den Bergh for surfaces. When X is projective, Plov(f) + 1 coincides with the Gelfand--Kirillov dimensions GKdim(X,f) of the twisted homogeneous coordinate rings associated to (X,f). Reformulating these results for GKdim(X,f), we impro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.03423","kind":"arxiv","version":4},"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/2104.03423/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"}