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A Uniqueness Property for H^{\infty} on Coverings of Projective Manifolds

A. Brudnyi
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Abstract

Let Y be a regular covering of a complex projective manifold M\hookrightarrow CP^{N} of dimension n\geq 2. Let C be intersection with M of at most n-1 generic hypersurfaces of degree d in CP^{N}. The preimage X of C in Y is a connected submanifold. Let H^{\infty}(Y) and H^{\infty}(X) be the Banach spaces of bounded holomorphic functions on Y and X in the corresponding supremum norms. We prove that the restriction H^{\infty}(Y)\longrightarrow H^{\infty}(X) is an isometry for d large enough. This answers the question posed in [L] by F. Larusson and strengthen his example of the Riemann surface with large corona.

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A. Brudnyi. 2002-04-05. A Uniqueness Property for H^{\infty} on Coverings of Projective Manifolds. https://arxiv.org/abs/math/0204073

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