Log-canonical threefold abundance in numerical dimension one

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.

Manuscripts (2)

Log abundance in numerical dimension one for threefolds in positive characteristic

October 5, 2026 · source · cite as \cite{OAI:Log-abundance-in-numerical-dimension-one-for-threefolds-in-positive-characteristic-October-5-2026}

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.

Abundance in numerical dimension one for terminal threefolds in positive characteristic

September 24, 2026 · source · cite as \cite{OAI:Abundance-in-numerical-dimension-one-for-terminal-threefolds-in-positive-characteristic-September-24-2026}

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.

Result 035 · Algebraic and complex geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.