∑math20

Algebraic and complex geometry · Result 051

Kobayashi’s canonical-ampleness conjecture

1 paper

Every compact connected Kähler manifold of positive complex dimension with no nonconstant entire curve has ample canonical bundle and is therefore projective. This proves Kobayashi's canonical-ampleness conjecture in the smooth compact Kähler setting.

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Papers 1

First page of Canonical ampleness of compact hyperbolic Kähler manifolds

Canonical ampleness of compact hyperbolic Kähler manifolds

OpenAI · September 23, 2026

We prove that every compact connected Kähler manifold of positive complex dimension containing no nonconstant entire curve has ample canonical bundle and is projective. This resolves positively Kobayashi's canonical-ampleness conjecture in the smooth compact Kähler category.

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@misc{OAI:Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026,
  author = {{OpenAI}},
  title = {{Canonical ampleness of compact hyperbolic K{\"a}hler manifolds}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026/canonical-ampleness.pdf}{OAI:Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026}},
  year = {2026}
}

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