OpenAI reports numerical-dimension-one log abundance in characteristic above three

For a projective log canonical threefold pair over an algebraically closed field of characteristic p > 3, if the rational log canonical divisor K_X+B is Q-Cartier, nef, and has numerical dimension one, then it is semiample.

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Understanding the problem

Read the background

For a projective log canonical threefold pair over an algebraically closed field of characteristic p > 3, if the rational log canonical divisor K_X+B is Q-Cartier, nef, and has numerical dimension one, then it is semiample.

Why it matters

If correct, establishes a new log abundance case for positive-characteristic threefolds without terminality or Q-factoriality of the original variety.

What counts as progress

Is a nef log canonical divisor of numerical dimension one semiample on a threefold in characteristic p > 3?

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