Relative $\dbar$-complex and its curvature properties

Abstract

We shall define the relative $\dbar$-complex and study the curvature properties of the associated vector bundles. As an application, we shall prove that Yamaguchi's theory on subharmonicity of the Green operator can be seen as a curvature property of the quotient bundle. A short survey of other recent applications will also be given in this paper.

8 pages

References in corpus (3)

• A simple proof of the Ohsawa-Takegoshi extension theorem
• A proof of the Ohsawa-Takegoshi theorem with sharp estimates
• Curvature of higher direct image sheaves and its application on negative-curvature criterion for the Weil-Petersson metric