Level 5: Minimal metrics and interior injectivity for nef adjoints

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LEVEL 5 OF 14 · Log abundance and effective Iitaka fibrations

Minimal metrics and interior injectivity for nef adjoints

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

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How to play: Let $(H,\Theta)$ be a projective complex klt pair with effective rational boundary and nef ℚ-Cartier adjoint. On any projective log resolution, minimal semipositive metrics on the pulled-back adjoint exist and have zero Lelong numbers everywhere. On smooth projective complex varieties, we also prove an H¹-injectivity theorem for rational interior boundaries with simple-normal-crossing support when both endpoint bundles carry zero-Lelong semipositive metrics.

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