Irregular slc Calabi–Yau boundary case

Resolve the remaining irregular case in the analysis of slc Calabi–Yau boundaries, namely the case where the slc Calabi–Yau boundary has nonzero irregularity, in order to complete the corresponding cohomological and semiampleness analysis.

Background

The paper studies abundance for projective log canonical threefolds in characteristic greater than 42. Its technical approach analyzes an slc Calabi–Yau surface boundary arising on a formal cover and separates cases according to the boundary’s cohomological behavior.

The authors explicitly state that the case of zero irregularity has been settled while identifying the irregular case as still unresolved. This is included because the passage contains the explicit marker “leaving open” and identifies a concrete remaining case.