| Title: | Oka-1 manifolds: new examples and properties |
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| Authors: | ID Forstnerič, Franc (Author)
ID Lárusson, Finnur (Author) |
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| Files: |  PDF - Presentation file, download (342,34 KB)
MD5: DF8EF062FDDA612768940E4705C4796D
 URL - Source URL, visit https://link.springer.com/article/10.1007/s00209-024-03649-8
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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 investigate Oka-1 manifolds and Oka-1 maps, a class of complex manifolds and holomorphic maps recently introduced by Alarcón and Forstnerič. Oka-1 manifolds are characterised by the property that holomorphic maps from any open Riemann surface to the manifold satisfy the Runge approximation and Weierstrass interpolation conditions, while Oka-1 maps enjoy similar properties for liftings of maps from open Riemann surfaces in the absence of topological obstructions. We also formulate and study the algebraic version of the Oka-1 condition, called aOka-1. We show that it is a birational invariant for compact algebraic manifolds and holds for all rational manifolds. This gives a Runge approximation theorem for maps from compact Riemann surfaces to uniformly rational projective manifolds. Finally, we study a class of complex manifolds with an approximation property for holomorphic sprays of discs. This class lies between the smaller class of Oka manifolds and the bigger class of Oka-1 manifolds and has interesting functorial properties. |
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| Keywords: | Riemann surfaces, complex manifolds, algebraic manifolds, Oka-1 manifolds, Oka manifolds, algebraically elliptic manifold, Runge approximation |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.02.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 16 str. |
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| Numbering: | Vol. 309, iss. 2, article no. 26 |
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| PID: | 20.500.12556/DiRROS-21157  |
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| UDC: | 517.5 |
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| ISSN on article: | 0025-5874 |
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| DOI: | 10.1007/s00209-024-03649-8 |
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| COBISS.SI-ID: | 220426499 |
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| Note: |
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| Publication date in DiRROS: | 08.01.2025 |
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| Views: | 655 |
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| Downloads: | 312 |
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