# [Numerical semiampleness of nef adjoint classes on compact Kähler manifolds](numerical-generalized-abundance.pdf)

**Author:** OpenAI

**Date:** October 6, 2026

## Citation

```bibtex
@misc{OAI:Numerical-semiampleness-of-nef-adjoint-classes-on-compact-Kahler-manifolds-October-6-2026,
  author = {{OpenAI}},
  title = {{Numerical semiampleness of nef adjoint classes on compact K{\"a}hler manifolds}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Numerical-semiampleness-of-nef-adjoint-classes-on-compact-Kahler-manifolds-October-6-2026/numerical-generalized-abundance.pdf}{OAI:Numerical-semiampleness-of-nef-adjoint-classes-on-compact-Kahler-manifolds-October-6-2026}},
  year = {2026}
}
```

## Version note

This version states the Iitaka, model, and contraction inputs used in the divisorial-decomposition argument explicitly; see the [previous version](../Numerical-semiampleness-of-nef-adjoint-classes-on-compact-Kahler-manifolds-October-4-2026/numerical-generalized-abundance.pdf).