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Recent developments on Oka manifolds (2006.07888v7)

Published 14 Jun 2020 in math.CV and math.AG

Abstract: 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 $\mathbb Cn$ in a Stein family can degenerate to a non-Oka fibre, thereby answering a question of Takeo Ohsawa. Several open problems are discussed.

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