{"paper":{"title":"Tropical Hopf manifolds and contracting germs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AG","authors_text":"Kristin Shaw, Matteo Ruggiero","submitted_at":"2015-09-13T00:01:04Z","abstract_excerpt":"Classical Hopf manifolds are compact complex manifolds whose universal covering is $\\mathbb{C}^d \\setminus \\{0\\}$. We investigate the tropical analogues of Hopf manifolds, and relate their geometry to tropical contracting germs. To do this we develop a procedure called monomialization which transforms non-degenerate tropical germs into morphisms, up to tropical modification. A link is provided between tropical Hopf manifolds and the analytification of Hopf manifolds over a non-archimedean field. We conclude by computing the tropical Picard group and $(p,q)$-homology groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03787","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"}