Bochner-Hartogs type extension theorem for roots and logarithms of   holomorphic line bundles
  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. 
Sergey Ivashkovich
math.CV math.AG