Extension of Jets With $L^2$ Estimates, and an Application

Abstract

We study the problem of extension of normal jets from a hypersurface, with focus on the growth order of the constant. Using aspects of the standard, twisted approach for $L^2$ extension and of the new approach to $L^2$ extension introduced by Berndtsson and Lempert, we are able to obtain an extension theorem with a constant $C^k$ where $C$ is universal and $k$ is the jet order. We then use the jet extension theorem to extend positively curved singular Hermitian metrics from smooth, deformably pseudoeffective hypersurfaces in projective manifolds.

The main result is incorrect. The authors thought the paper was withdrawn long ago, but something went wrong with the processing in ArXiV

Cited by in corpus (5)

• On the Ohsawa-Takegoshi extension theorem
• A simplified proof of optimal $L^2$-extension theorem and extensions from non-reduced subvarieties
• On the extensions of Kähler currents on compact Kähler manifolds
• Lelong numbers and vector bundles
• On sharper estimates of Ohsawa-Takegoshi $L^2$-extension theorem