Log-canonical threefold abundance in numerical dimension one
OpenAI research collection · 2 manuscripts · Source checked 2026-10-19
OpenAI's result summary
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.
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MANUSCRIPT 01
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 K_X+B is ℚ-Cartier, nef, and of numerical dimension one, then K_X+B is semiample. Neither terminality nor…
Full source 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.
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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 K_(X) is nef with \nu(K_X)=1, then K_(X) is semiample and \kappa(X,K_X)=1.
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