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A theorem of \(L^ 2\) extension of holomorphic sections of a Hermitian bundle. (Un théorème de prolongement \(L^ 2\) de sections holomorphes d’un fibré hermitien.) (French) Zbl 0789.32015
Let \(Y\) be a subvariety of a Stein variety \(X\), defined by a holomorphic section of a vector bundle \(E\), having generically a differential of maximal rank. We give sufficient conditions on the curvature of a hermitian line bundle \(L\), for any section of the line bundle \(K_ Y \otimes L \otimes (\text{det} E)^{-1}\) to extend to a section of \(K_ X \otimes L\) on \(X\), with \(L^ 2\) estimates. When \(X\) is a projective variety, we get a purely algebraic condition for the restriction morphism \(H^ 0(X,L) \to H^ 0(Y,L)\) to be surjective.

MSC:
32Q20 Kähler-Einstein manifolds
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