oai-math-revised beta

Browse › Algebraic and complex geometry › 034 Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity

Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity

OpenAI · 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

Abstract

Assume logarithmic Iitaka subadditivity for surjective morphisms with connected fibers between smooth projective complex varieties with compatible reduced simple normal crossing boundaries. We prove log abundance for normal irreducible compact Kähler spaces in every dimension: for a log canonical pair $(X,\Delta)$ with effective rational boundary and $K_X+\Delta$ ℚ-Cartier, analytic nefness of $K_X+\Delta$ implies semiampleness.

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.

Automatically collected notes (unreviewed)

work in progress

Collected automatically by AI tools (Claude Opus 5.5 and GPT-6 Astra, 2026-10-21) and not checked by a person. May be wrong or incomplete. Report an error.

Possibly relevant literature (found by the agent, not checked)

Digests and expositions

  • AI Proved What?, Always semiample? (Episode 034, October 2026). Explains the family’s abundance claims, proof strategy, and dependencies. [AI-generated per source] [family-level]

Elsewhere

Independent sites; their content is not reviewed here.

Cite

@misc{OAI:Log-abundance-for-compact-Kahler-spaces-under-logarithmic-Iitaka-subadditivity-October-6-2026,
  author = {{OpenAI}},
  title = {{Log abundance for compact K{\"a}hler spaces under logarithmic Iitaka subadditivity}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Log-abundance-for-compact-Kahler-spaces-under-logarithmic-Iitaka-subadditivity-October-6-2026/main.pdf}{OAI:Log-abundance-for-compact-Kahler-spaces-under-logarithmic-Iitaka-subadditivity-October-6-2026}},
  year = {2026}
}

Versions

This version supplies base-presentation and multiplier-ideal arguments for the induction, including the adjoint pullback and contraction-descent steps; see the previous version.

Family 034: Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity

Using logarithmic Iitaka subadditivity, proves log abundance in every dimension for normal compact Kähler log canonical pairs with effective rational boundary: an analytically nef ℚ-Cartier adjoint is semiample. It also proves projective log abundance over every algebraically closed field of characteristic zero and the effective Iitaka fibration conjecture for smooth projective varieties of nonnegative Kodaira dimension in that setting. A further result resolves the finite-rational-coefficient index conjecture for connected projective semi-log-canonical log Calabi–Yau pairs over such fields in each fixed dimension and for each fixed finite set of rational boundary coefficients, with a uniform index independent of the number of components.

Other papers in this family: