Family 035Algebraic and complex geometryNo LeanNot yet digested
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 in this family · 2
Log abundance in numerical dimension one for threefolds in positive characteristic
Oct 5, 2026·paper.pdf
We prove the numerical-dimension-one case of log abundance for threefolds over algebraically closed fields of characteristic p > 3. If is a projective log canonical threefold pair with effective rational boundary, and is ℚ-Cartier, nef, and of numerical dimension one, then is semiample. Neither terminality nor ℚ-factoriality of X is required.
Abundance in numerical dimension one for terminal threefolds in positive characteristic
Sep 24, 2026·paper.pdf
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 is nef with , then K is semiample and .