Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 035-01. Log abundance in numerical dimension one for threefolds in positive characteristic
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OpenAI@2026-10-07#rem:oai-p-035-01
Authors: OpenAI. Family 035.
Title: Log abundance in numerical dimension one for threefolds in positive characteristic.
Abstract: We prove the numerical-dimension-one case of log abundance for threefolds over algebraically closed fields of characteristic p > 3. If $(X,B)$ is a projective log canonical threefold pair with effective rational boundary, and $K_X+B$ is ℚ-Cartier, nef, and of numerical dimension one, then $K_X+B$ is semiample. Neither terminality nor ℚ-factoriality of X is required.
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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