A Uniqueness Property for H^∞ on Coverings of Projective Manifolds

2002/04/05 by Alex Brudnyi, Brudnyi, A.
Mathematics · #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0204073

Abstract

Let Y be a regular covering of a complex projective manifold M\hookrightarrow CP^N of dimension n≥ 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^∞(Y) and H^∞(X) be the Banach spaces of bounded holomorphic functions on Y and X in the corresponding supremum norms. We prove that the restriction H^∞(Y)\longrightarrow H^∞(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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