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locally closed submanifold ocally Stein quasi-Stein 2024
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locally closed submanifold locally Stein quasi-Stein 2024
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最後の文献に、”thereby answering a question of Takeo Ohsawa”とありますね
外部ﾘﾝｸ:arxiv.org
ON THE FIELD OF MEROMORPHIC FUNCTIONS ON A STEIN SURFACE
arXiv:2410.16809v1 [math.AG] 22 Oct 2024
OLIVIER BENOIST
Abstract.
We prove that fields of meromorphic functions on Stein surfaces have cohomological dimension 2, and solve the period-index problem and Serre’s conjecture II for these fields. We obtain analogous results for fields of real meromorphic functions on Stein surfaces equipped with an antiholomorphic involution. We deduce an optimal quantitative solution to Hilbert’s 17th problem on analytic surfaces.
外部ﾘﾝｸ:link.springer.com
Springer Nature Link
Oka-1 manifolds: New examples and properties
Open access
Published: 23 December 2024
Volume 309, article number 26, (2025)
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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