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Fujita’s freeness conjecture

The sharp n+1 threshold was known in several low dimensions, while general-dimensional results required larger twists.

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Understand the problem ↓

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Understanding the problem

Read the background

The sharp n+1 threshold was known in several low dimensions, while general-dimensional results required larger twists. The targeted advance attains the sharp threshold in every dimension.

Global generation is weaker than very ampleness. The claim does not settle the separate very-ampleness assertion, and the smooth complex-projective hypotheses matter.

Why it matters

If correct, attains the sharp general-dimensional global-generation threshold predicted by Fujita’s freeness conjecture.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • Global generation is weaker than very ampleness. The claim does not settle the separate very-ampleness assertion, and the smooth complex-projective hypotheses matter.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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