Fujita’s freeness conjecture

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.

Manuscript

Fujita's freeness conjecture

September 23, 2026 · source · cite as \cite{OAI:Fujitas-freeness-conjecture-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.

Result 038 · Algebraic and complex geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Agora members.