On the complement of a hypersurface with flat normal bundle which corresponds to a semipositive line bundle

TL;DR

This paper studies the complex structure of the space outside a smooth hypersurface with a flat normal bundle, focusing on cases where the associated line bundle has a semipositive Hermitian metric, revealing new geometric insights.

Contribution

It provides new results on the complex analytic properties of hypersurface complements with semipositive line bundles and flat normal bundles, extending previous understanding in complex geometry.

Findings

Characterization of the complex structure of hypersurface complements

Conditions under which the line bundle admits a semipositive Hermitian metric

Implications for the geometry of the complement space

Abstract

We investigate the complex analytic structure of the complement of a non-singular hypersurface with unitary flat normal bundle when the corresponding line bundle admits a Hermitian metric with semipositive curvature.