Algebraic Gromov Ellipticity: A Brief Survey

Zaidenberg, Mikhail

doi:10.11650/tjm/241001

Taiwanese J. Math.

2024

DOI: 10.11650/tjm/241001

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Algebraic Gromov Ellipticity: A Brief Survey

Mikhail Zaidenberg

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2024

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Oka-1 manifolds: New examples and properties

Forstnerič,

Lárusson

2024

Math. Z.

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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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Oka-1 manifolds: New examples and properties

Forstnerič,

Lárusson

2024

Math. Z.

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Algebraic Gromov Ellipticity: A Brief Survey

Cited by 1 publication

References 66 publications

Oka-1 manifolds: New examples and properties

Oka-1 manifolds: New examples and properties

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