Year: 2025
Type: article
Abstract: Let 𝑀 be an open Riemann surface and 𝐴 the punctured cone in C n ∖ { 0 } \mathbb{C}^{n}\setminus\{0\} on a smooth projective variety 𝑌 in P n − 1 \mathbb{P}^{n-1} . Recently, Runge approximation theorems with interpolation for holomorphic immersions M → C n M\to\mathbb{C}^{n} , directed by 𝐴, have been proved under the assumption that 𝐴 is an Oka manifold. We prove analogous results in the algebraic setting, for regular immersions directed by 𝐴 from a smooth affine curve 𝑀 into C n \mathbb{C}^{n} . The Oka property is naturally replaced by the stronger assumption that 𝐴 is algebraically elliptic, which it is if 𝑌 is uniformly rational. Under this assumption, a homotopy-theoretic necessary and sufficient condition for approximation and interpolation emerges. We show that this condition is satisfied in many cases of interest.
Authors: Antonio Alarcón, Finnur Lárusson
Institutions: Universidad de Granada, The University of Adelaide
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408318427