An extension theorem for hermitian line bundles

TL;DR

This paper proves a general extension theorem for holomorphic line bundles with singular hermitian metrics on complex spaces, enabling the extension of curvature currents and impacting moduli theory.

Contribution

It introduces a new extension theorem for hermitian line bundles with singular metrics, broadening the scope of extension results in complex geometry.

Findings

Extension of curvature currents as positive, closed currents

Applicability to moduli problems in complex geometry

Generalization of existing extension theorems

Abstract

We prove a general extension theorem for holomorphic line bundles on reduced complex spaces, equipped with singular hermitian metrics, whose curvature currents can be extended as positive, closed currents. The result has applications to various moduli theoretic situations.