Oka-1 manifolds: new examples and properties

Forstnerič, Franc (avtor), Lárusson, Finnur (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: Riemann surfaces, complex manifolds, algebraic manifolds, Oka-1 manifolds, Oka manifolds, algebraically elliptic manifold, Runge approximation
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2025
• Št. strani: 16 str.
• Številčenje: Vol. 309, iss. 2, art. 26
• PID: 20.500.12556/RUL-166348
• UDK: 517.5
• ISSN pri članku: 0025-5874
• DOI: 10.1007/s00209-024-03649-8
• COBISS.SI-ID: 220426499
• Datum objave v RUL: 08.01.2025

Gradivo je del revije

• Naslov: Mathematische Zeitschrift
• Skrajšan naslov: Math. Z.
• Založnik: Springer Nature
• ISSN: 0025-5874
• COBISS.SI-ID: 25915904

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: Riemannove ploskve, kompleksne mnogoterosti, algebraične mnogoterosti, Oka-1 mnogoterosti, Oka mnogoterosti, algebraično eliptična mnogoterost, Rungejeva aproksimacija