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

Uniform Pluricanonical Iitaka Fibrations

OpenAI · October 3, 2026

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Abstract

We prove the effective Iitaka fibration conjecture in characteristic zero. For each dimension, one pluricanonical degree defines the Iitaka fibration of every smooth integral projective variety of that dimension and nonnegative Kodaira dimension over an algebraically closed field. The associated sections generate the full Iitaka function field.

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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

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Cite

@misc{OAI:Uniform-Pluricanonical-Iitaka-Fibrations-October-3-2026,
  author = {{OpenAI}},
  title = {{Uniform Pluricanonical Iitaka Fibrations}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Uniform-Pluricanonical-Iitaka-Fibrations-October-3-2026/paper.pdf}{OAI:Uniform-Pluricanonical-Iitaka-Fibrations-October-3-2026}},
  year = {2026}
}

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.

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