Varieties covered by affine spaces, uniformly rational varieties and their cones

Arzhantsev, I.; Kaliman, S.; Zaidenberg, M.

doi:10.1016/j.aim.2023.109449

Advances in Mathematics

2024

DOI: 10.1016/j.aim.2023.109449

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Varieties covered by affine spaces, uniformly rational varieties and their cones

I. Arzhantsev,

S. Kaliman,

M. Zaidenberg

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2024

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Cited by 3 publications

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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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Images of dominant endomorphisms of affine space

Balch Barth,

Truong

2024

Communications in Algebra

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Algebraic Gromov Ellipticity: A Brief Survey

Zaidenberg

2024

Taiwanese J. Math.

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Varieties covered by affine spaces, uniformly rational varieties and their cones

Cited by 3 publications

References 21 publications

Oka-1 manifolds: New examples and properties

Oka-1 manifolds: New examples and properties

Images of dominant endomorphisms of affine space

Algebraic Gromov Ellipticity: A Brief Survey

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