Recent developments on Oka manifolds

Forstnerič, Franc (author)

In this paper we present the main developments in Oka theory since the publication of my book Stein Manifolds and Holomorphic Mappings (The Homotopy Principle in Complex Analysis), Second Edition, Springer, 2017. We also give several new results, examples and constructions of Oka domains in Euclidean and projective spaces. Furthermore, we show that for $n > 1$ the fibre $\mathbb C^n$ in a Stein family can degenerate to a non-Oka fibre, thereby answering a question of Takeo Ohsawa. Several open problems are discussed.

• Language: English
• Keywords: Oka manifold, Oka map, Stein manifold, elliptic manifold, algebraically subelliptic manifold, Calabi–Yau manifold, density property
• Work type: Article
• Typology: 1.02 - Review Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: Str. 367-417
• Numbering: Vol. 34, iss. 2
• PID: 20.500.12556/RUL-148319-4f4d35ad-da25-3733-986d-42e4edd4c27c
• UDC: 517.5
• ISSN on article: 0019-3577
• DOI: 10.1016/j.indag.2023.01.005
• COBISS.SI-ID: 140663299
• Publication date in RUL: 11.08.2023

Record is a part of a journal

• Title: Indagationes mathematicae
• Shortened title: Indag. math.
• Publisher: Elsevier, Royal Dutch Mathematical Society (KWG)
• ISSN: 0019-3577
• COBISS.SI-ID: 25594112

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: Okova mnogoterost, Okova preslikava, Steinova mnogoterost, eliptična mnogoterost, algebraično subeliptična mnogoterost, Calabi–Yaujeva mnogoterost, lastnost gostote