Algebraic and complex geometry · Result 038

Fujita’s freeness conjecture

1 paper

Proves Fujita's freeness conjecture at its sharp bound in every dimension: for a smooth projective complex variety X of dimension n and an ample line bundle L, the adjoint \(K_X+mL\) is globally generated for every integer \(m\ge n+1\).

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The problem

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Papers 1

Fujita's freeness conjecture

OpenAI · September 23, 2026

We prove Fujita's freeness conjecture. If X is a smooth complex projective variety of dimension n and L is an ample line bundle, then \(K_X+mL\) is globally generated for every integer \(m\geq n+1\).

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@misc{OAI:Fujitas-freeness-conjecture-September-23-2026,
  author = {{OpenAI}},
  title = {{Fujita's freeness conjecture}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Fujitas-freeness-conjecture-September-23-2026/Fujitas-freeness-conjecture-September-23-2026.pdf}{OAI:Fujitas-freeness-conjecture-September-23-2026}},
  year = {2026}
}

Formal verification

No Lean formalization is listed for this result yet. The repository notes that unformalized results could have issues.