{"paper":{"title":"An upper bound for polynomial volume growth of automorphisms of zero entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.RA"],"primary_cat":"math.AG","authors_text":"Chen Jiang, Fei Hu","submitted_at":"2024-08-28T14:01:26Z","abstract_excerpt":"Let $X$ be a normal projective variety of dimension $d$ over an algebraically closed field and $f$ an automorphism of $X$. Suppose that the pullback $f^*|_{\\mathsf{N}^1(X)_\\mathbf{R}}$ of $f$ on the real N\\'eron--Severi space $\\mathsf{N}^1(X)_\\mathbf{R}$ is unipotent and denote the index of the eigenvalue $1$ by $k+1$. We establish the following upper bound for the polynomial volume growth $\\mathrm{plov}(f)$ of $f$: \\[ \\mathrm{plov}(f) \\le (k/2 + 1)d. \\] This inequality is optimal in certain cases. Moreover, we prove that $k\\le 2(d-1)$, extending a result of Dinh--Lin--Oguiso--Zhang for compac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.15804","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"}