{"paper":{"title":"On the virtual invariants of zero entropy groups of compact K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DS"],"primary_cat":"math.AG","authors_text":"De-Qi Zhang, Hsueh-Yung Lin, Keiji Oguiso, Tien-Cuong Dinh","submitted_at":"2023-10-08T03:05:43Z","abstract_excerpt":"Let $X$ be a compact K\\\"ahler manifold. We study subgroups $G \\le \\mathrm{Aut}(X)$ of biholomorphic automorphisms of zero entropy when $\\mathrm{Aut}^0(X)$ is compact (e.g. when $\\mathrm{Aut}^0(X)$ is trivial). We show that the virtual derived length $\\ell_{\\mathrm{vir}}(G)$ of $G$ satisfies $\\ell_{\\mathrm{vir}}(G) \\le \\dim X -\\kappa(X)$, where $\\kappa(X)$ is the Kodaira dimension of $X$. Modulo the main conjecture of our previous work concerning the essential nilpotency class, we obtain the same upper bound $c_{\\mathrm{vir}}(G) \\le \\dim X -\\kappa(X)$ for the virtual nilpotency class $c_{\\mathr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.04980","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.04980/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"}