{"paper":{"title":"Algebraic dynamics of skew-linear self-maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AG","authors_text":"Dragos Ghioca, Junyi Xie","submitted_at":"2018-03-11T10:13:56Z","abstract_excerpt":"Let $X$ be a variety defined over an algebraically closed field $k$ of characteristic $0$, let $N\\in\\mathbb{N}$, let $g:X\\dashrightarrow X$ be a dominant rational self-map, and let $A:\\mathbb{A}^N\\to \\mathbb{A}^N$ be a linear transformation defined over $k(X)$, i.e., for a Zariski open dense subset $U\\subset X$, we have that for $x\\in U(k)$, the specialization $A(x)$ is an $N$-by-$N$ matrix with entries in $k$. We let $f:X\\times\\mathbb{A}^N\\dashrightarrow X\\times \\mathbb{A}^N$ be the rational endomorphism given by $(x,y)\\mapsto (g(x), A(x)y)$. We prove that if the determinant of $A$ is nonzero"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03931","kind":"arxiv","version":1},"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"}