Algebraic and complex geometry·OpenAI Math·Result 035
Log-canonical threefold abundance in numerical dimension one
One of the 372 results in OpenAI's public mathematics catalogue, filed under algebraic and complex geometry: 2 preprints, the latest dated 5 October 2026. This page quotes OpenAI's own summary of the claim, links the papers and abstracts, and will embed the animation.
Latest paper
Log abundance in numerical dimension one for threefolds in positive characteristic
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What OpenAI claims
Proves log abundance for projective log canonical threefold pairs over algebraically closed fields of characteristic p > 3 when the effective boundary is rational and the ℚ-Cartier adjoint is nef of numerical dimension one. The adjoint is semiample, without requiring the original variety to be terminal or ℚ-factorial.
Papers (2)
Log abundance in numerical dimension one for threefolds in positive characteristic
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 KX+B is ℚ-Cartier, nef, and of numerical dimension one, then KX+B is semiample. Neither terminality nor ℚ-factoriality of X is required.
Abundance in numerical dimension one for terminal threefolds in positive characteristic
Let X be a projective ℚ-factorial terminal threefold over an algebraically closed field of characteristic p > 3. We prove the numerical-dimension-one case of abundance: if KX is nef with ν(KX)=1, then KX is semiample and κ(X,KX)=1.
Status
Preprint. The papers have not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
