| Title: | The universal family of punctured Riemann surfaces is Stein |
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| Authors: | ID Forstnerič, Franc (Author) |
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| Files: |  PDF - Presentation file, download (329,06 KB)
MD5: 9AEF4EC70E89B2E05A6C7F34BBA7BDF5
 URL - Source URL, visit https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/blms.70383
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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: | We show that the universal Teichmüller family $V(g, n)$ of compact Riemann surfaces of genus $g \ge 0$ with $n > 0$ punctures is a Stein manifold. We describe its basic function-theoretic properties and pose some challenging questions. We show, in particular, that the space of fibrewise algebraic functions on the universal family is dense in the space of holomorphic functions, and that there is a fibrewise algebraic map of the universal family to a Euclidean space which restricts to a proper embedding on any fibre. We also obtain a relative Oka principle for holomorphic fibrewise algebraic maps of the universal family to any flexible algebraic manifold. |
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| Keywords: | Riemann surfaces, Teichmüller space, universal family, Steinova manifold, Oka manifold |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.05.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | 16 str. |
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| Numbering: | Vol. 58, iss. 5, article no. e70383 |
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| PID: | 20.500.12556/DiRROS-29489  |
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| UDC: | 517.5 |
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| ISSN on article: | 0024-6093 |
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| DOI: | 10.1112/blms.70383 |
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| COBISS.SI-ID: | 278869507 |
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| Note: |
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| Publication date in DiRROS: | 21.05.2026 |
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| Views: | 40 |
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| Downloads: | 21 |
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