{"paper":{"title":"The dimension of automorphism groups of algebraic varieties with pseudo-effective log canonical divisors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Fei Hu","submitted_at":"2016-11-03T03:56:09Z","abstract_excerpt":"Let $(X,D)$ be a log smooth pair of dimension $n$, where $D$ is a reduced effective divisor such that the log canonical divisor $K_X + D$ is pseudo-effective. Let $G$ be a connected algebraic subgroup of $\\mathrm{Aut}(X,D)$. We show that $G$ is a semi-abelian variety of dimension $\\le \\min\\{n-\\bar{\\kappa}(V), n\\}$ with $V := X\\setminus D$. In the dimension two, Shigeru Iitaka claimed in his 1979 Osaka J. Math. paper that $\\dim G\\le \\bar{q}(V)$ for a log smooth surface pair with $\\bar{\\kappa}(V) = 0$ and $\\bar{p}_g(V) = 1$. We (re)prove and generalize this classical result for all surfaces with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00875","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"}