An extension theorem of Ohsawa-Takegoshi type for sections of a vector bundle

Abstract

Using $L^2$-methods for the $\bar{\partial }$-equation we prove that the Ohsawa-Takegoshi extension theorem also holds for holomorphic sections of a vector bundle, over compact Kähler manifolds. We then proceed to show that the conditions that are needed are more liberal than the ones one would need if one instead reduced the extension problem to line bundles through the usual algebraic geometric procedure of studying the projective bundle associated with the vector bundle.

18 pages

References in corpus (1)

• The Nakano vanishing theorem and a vanishing theorem of Demailly-Nadel type for holomorphic vector bundles

Cited by in corpus (1)

• Asymptotic estimate of cohomology groups valued in pseudo-effective line bundles