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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In Fujita’s freeness conjecture, 23 September 2026
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Let X be a smooth connected projective variety over \C of dimension n\geq 1, and let L be an ample line bundle on X. Then
is generated by its global sections.
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Theorem 1.1
In Fujita’s freeness conjecture, 23 September 2026