Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 068-06. Integrable metrics and effectivity with controlled boundary
Manuscript map · lines 3855–3864
OpenAI@2026-10-07#rem:oai-p-068-06
Authors: OpenAI. Family 068.
Title: Integrable metrics and effectivity with controlled boundary.
Abstract: Let Y be smooth projective and let C be an effective integral divisor. If $-K_Y+C$ admits a metric with a global strict curvature lower bound for which the canonical section of C is locally square integrable, every pseudoeffective rational divisor becomes rationally effective after an effective correction supported on C. For a smooth projective X with smoothly semipositive $L=-K_X$, sections of $m_jL-P$ at unbounded positive exponents, with any fixed pseudoeffective Cartier error P, yield a section of a positive multiple of L.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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