oai-math-revised beta

Browse › Algebraic and complex geometry › 036 Numerical semiampleness and generalized minimal models

Numerical semiampleness of nef adjoint classes on compact Kähler manifolds

OpenAI · October 4, 2026

Earlier edition

This is an earlier edition (October 4, 2026). Current edition: Numerical semiampleness of nef adjoint classes on compact Kähler manifolds, October 6, 2026.

Open PDFCite Report a problem Add a reference or comment Interested in working on this Start a discussion

Edit NOTES.md · Existing issues · Source on GitHub

If the PDF does not display here, open it directly: Open PDF.

Notes

No notes yet. Add a reference, a comment or your name with the buttons above, or edit NOTES.md on GitHub.

Elsewhere

Independent sites; their content is not reviewed here.

Cite

@misc{OAI:Numerical-semiampleness-of-nef-adjoint-classes-on-compact-Kahler-manifolds-October-4-2026,
  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-4-2026/numerical-generalized-abundance.pdf}{OAI:Numerical-semiampleness-of-nef-adjoint-classes-on-compact-Kahler-manifolds-October-4-2026}},
  year = {2026}
}

Family 036: Numerical semiampleness and generalized minimal models

Proves numerical semiampleness for nef adjoints $K_X+B+M$ with $K_X+B$ pseudo-effective and M nef rational, for projective klt rational pairs over algebraically closed characteristic-zero fields and smooth compact Kähler rational klt simple-normal-crossing pairs, using Bott–Chern cohomology in the latter case. Separately, projective generalized log canonical rational pairs over such fields admit minimal models for pseudo-effective adjoints and Mori fiber spaces otherwise, with nef b-data fixed.

Other papers in this family: