{"paper":{"title":"On the Medvedev-Scanlon Conjecture for Minimal Threefolds of Non-Negative Kodaira Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NT"],"primary_cat":"math.AG","authors_text":"Dragos Ghioca, Jason P. Bell, Matthew Satriano, Zinovy Reichstein","submitted_at":"2016-10-12T20:01:05Z","abstract_excerpt":"Motivated by work of Zhang from the early `90s, Medvedev and Scanlon formulated the following conjecture. Let $K$ be an algebraically closed field of characteristic $0$ and let $X$ be a quasiprojective variety defined over $K$ endowed with a dominant rational self-map $\\Phi$. Then there exists a point $\\alpha\\in X(K)$ with Zariski dense orbit under $\\Phi$ if and only if $\\Phi$ preserves no nontrivial rational fibration, i.e., there exists no non-constant rational function $f\\in K(X)$ such that $\\Phi^*(f)=f$. The Medvedev-Scanlon conjecture holds when $K$ is uncountable. The case where $K$ is c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03858","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"}