An extension theorem for holomorphic functions of slow growth on covering spaces of projective manifolds (Q1897239)

Let \(X\) be a projective manifold of dimension \(n \geq 2\) and \(Y \to X\) be an infinite covering space. Embed \(X\) into projective space by sections of a sufficiently ample line bundle. We prove that any holomorphic function of sufficiently slow growth on the preimage of a transverse intersection of \(X\) by a linear subspace of codimension \(< n\) extends to \(Y\). The proof uses a Hausdorff duality theorem for \(L_2\) cohomology. We also show that every projective manifold has a finite branched covering whose universal covering space is Stein.