Tight approximation for rationally simply connected varieties

2025/03/13 by Olivier Benoist, Olivier Wittenberg, Benoist, Olivier +1 · 3 citations
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2503.10564

Abstract

We prove that holomorphic maps from an open subset of a complex smooth projective curve to a complex smooth projective rationally simply connected variety can be approximated by algebraic maps for the compact-open topology. This theorem can be applied in particular when the target is a smooth hypersurface of degree d in Pⁿ with n greater than or equal to d²-1. We deduce it from a more general result: the tight approximation property holds for rationally simply connected varieties over function fields of complex curves.

Citations

• Oka-1 manifolds: New examples and properties

Cited by

• Oka-1 manifolds
• Rationally Simply Connected Hypersurfaces in Orthogonal Grassmannians
• Generating all Ahlfors currents by a single entire curve
• From Stein manifolds to Oka manifolds: the h-principle in complex analysis

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