A soft Oka principle for proper holomorphic embeddings of open Riemann surfaces into (ℂ^*)²

2014/03/26 by Tyson Ritter, Ritter, Tyson
Mathematics · #32G05 #32H35 #32M17 #32Q40 #32Q55 #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Holomorphic and Operator Theory #Primary 32H02. Secondary 32C22

paper · pdf · doi:10.48550/arxiv.1403.6630

openalex publication_date 2014/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be an open Riemann surface. We prove an Oka property on the approximation and interpolation of continuous maps X → (ℂ^*)² by proper holomorphic embeddings, provided that we permit a smooth deformation of the complex structure on X outside a certain set. This generalises and strengthens a recent result of Alarcon and Lopez. We also give a Forstneric-Wold theorem for proper holomorphic embeddings (with respect to the given complex structure) of certain open Riemann surfaces into (ℂ^*)².

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