{"paper":{"title":"Holomorphic Flexibility Properties of Spaces of Elliptic Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David Bowman","submitted_at":"2016-09-22T22:58:38Z","abstract_excerpt":"Let $X$ be an elliptic curve and $\\mathbb{P}$ the Riemann sphere. Since $X$ is compact, it is a deep theorem of Douady that the set $\\mathcal{O}(X,\\mathbb{P})$ consisting of holomorphic maps $X\\to \\mathbb{P}$ admits a complex structure. If $R_n$ denotes the set of maps of degree $n$, then Namba has shown for $n\\geq2$ that $R_n$ is a $2n$-dimensional complex manifold. We study holomorphic flexibility properties of the spaces $R_2$ and $R_3$. Firstly, we show that $R_2$ is homogeneous and hence an Oka manifold. Secondly, we present our main theorem, that there is a $6$-sheeted branched covering "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07184","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"}