English

On the Log Abundance for Compact {K{\"a}hler} threefolds II

Algebraic Geometry 2025-06-13 v4 Complex Variables

Abstract

In this article we show that if (X,Δ)(X, \Delta) is a log canonical compact K\"ahler threefold pair such that KX+ΔK_X+\Delta is nef and the numerical dimension ν(X,KX+Δ)=2\nu(X, K_X+\Delta)=2, then KX+ΔK_X+\Delta is semi-ample. This result combined with our previous work in arXiv:2201.01202 shows that the log abundance holds for log canonical compact K\"ahler threefold pairs.

Keywords

Cite

@article{arxiv.2306.00671,
  title  = {On the Log Abundance for Compact {K{\"a}hler} threefolds II},
  author = {Omprokash Das and Wenhao Ou},
  journal= {arXiv preprint arXiv:2306.00671},
  year   = {2025}
}