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Bibliographic Details
Main Authors: Benoist, Olivier, Wittenberg, Olivier
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2503.10564
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author Benoist, Olivier
Wittenberg, Olivier
author_facet Benoist, Olivier
Wittenberg, Olivier
contents 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 P^n with n greater than or equal to d^2-1. We deduce it from a more general result: the tight approximation property holds for rationally simply connected varieties over function fields of complex curves.
format Preprint
id arxiv_https___arxiv_org_abs_2503_10564
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Tight approximation for rationally simply connected varieties
Benoist, Olivier
Wittenberg, Olivier
Algebraic Geometry
Complex Variables
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 P^n with n greater than or equal to d^2-1. We deduce it from a more general result: the tight approximation property holds for rationally simply connected varieties over function fields of complex curves.
title Tight approximation for rationally simply connected varieties
topic Algebraic Geometry
Complex Variables
url https://arxiv.org/abs/2503.10564