OpenAI · 038-01 · 2026-09-23 · Algebraic and complex geometry

Fujita's freeness conjecture

preprints/Fujitas-freeness-conjecture-September-23-2026

Family 038. Fujita's freeness conjecture.

The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.

Read against the standing problems

Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N

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 $K_{X} + m L$ is globally generated for every integer $m \geq n + 1$ .

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 $K_{X} + m L$ is globally generated for every integer $m \geq n + 1$ .

Preprint source and Lean scope

The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.

No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.