| Title: | Oka-1 manifolds |
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| Authors: | ID Alarcón, Antonio (Author)
ID Forstnerič, Franc (Author) |
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| Files: |  PDF - Presentation file, download (940,54 KB)
MD5: FB49F9FF89FB6475E8DF98A7F4729B7D
 URL - Source URL, visit https://link.springer.com/article/10.1007/s00209-025-03833-4
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | In this paper we begin a systematic study of the class of complex manifolds which are universal targets of holomorphic maps from open Riemann surfaces. We call them Oka-1 manifolds, by analogy with Oka manifolds that are universal targets of holomorphic maps from Stein manifolds of arbitrary dimension. We prove that every complex manifold which is dominable at most points by spanning tubes of complex lines in affine spaces is an Oka-1 manifold. In particular, a manifold dominable by ${\mathbb C}^n$ at most points is an Oka-1 manifold. We provide many examples of Oka-1 manifolds among compact complex surfaces, including all Kummer surfaces and all elliptic K3 surfaces. We show that the class of Oka-1 manifolds is invariant under Oka-1 maps inducing a surjective homomorphism of fundamental groups; this includes holomorphic fibre bundles with connected Oka fibres. In another direction, we prove that every bordered Riemann surface admits a holomorphic map with dense image in any connected complex manifold. The analogous result is shown for holomorphic Legendrian immersions in an arbitrary connected complex contact manifold. |
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| Keywords: | Riemann surfaces, complex curves, Oka-1 manifolds, Oka manifolds, K3 surfaces |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.10.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 34 str. |
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| Numbering: | Vol. 311, iss. 2, article no. 33 |
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| PID: | 20.500.12556/DiRROS-23373  |
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| UDC: | 517.5 |
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| ISSN on article: | 0025-5874 |
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| DOI: | 10.1007/s00209-025-03833-4 |
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| COBISS.SI-ID: | 246247171 |
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| Note: |
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| Publication date in DiRROS: | 22.08.2025 |
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| Views: | 227 |
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| Downloads: | 117 |
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