Article Dans Une Revue Taiwanese Journal of Mathematics, TJM Année : 2025

Tight approximation for rationally simply connected varieties

Résumé

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.

Dates et versions

hal-05367673 , version 1 (16-11-2025)

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Olivier Benoist, Olivier Wittenberg. Tight approximation for rationally simply connected varieties. Taiwanese Journal of Mathematics, TJM, In press. ⟨hal-05367673⟩
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