Bochner-Hartogs type extension theorem for roots and logarithms of holomorphic line bundles

TL;DR

This paper proves an extension theorem for roots and logarithms of holomorphic line bundles across pseudoconcave boundaries, identifying specific obstructions in certain low-dimensional cases.

Contribution

It establishes a comprehensive extension theorem for roots and logarithms of line bundles, including explicit obstructions in the critical two-dimensional case.

Findings

Extensions generally possible across pseudoconcave boundaries

Explicit description of obstructions in the two-dimensional case

Identification of a unique exception based on dimension and Morse index

Abstract

We prove an extension theorem for roots and logarithms of holomorphic line bundles across strictly pseudoconcave boundaries: they extend in all cases except one, when dimension and Morse index of a critical point is two. In that case we give an explicit description of obstructions to the extension.