Level 7: Lifting sections from the reduced support of an adjoint

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LEVEL 7 OF 14 · Log abundance and effective Iitaka fibrations

Lifting sections from the reduced support of an adjoint

expertly designed by an internal OpenAI model · released 2026-09-27 · original PDF

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How to play: For a projective ℚ-factorial dlt pair with effective rational boundary over an algebraically closed field of characteristic zero, we prove that the adjoint has positive Iitaka dimension whenever a nonzero effective Cartier multiple is supported on the coefficient-one boundary and restricts to a semiample line bundle on its whole reduced support. This gives log abundance after nonvanishing in dimension at most four over ℂ.

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