Regular quantizations and covering maps

LOI, ANDREA

2006-01-01

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Abstract

Let \tilde M-->M be a holomorphic (unbranched) covering map between two compact complex manifolds, with b_2(\tilde M)=1. We prove that if \tilde M and M both admit regular Kaehler forms \tilde\omega and \omega respectively then, up to homotheties, (\tilde M, \tilde\omega) and (M, \omega) are biholomorphically isometric.