Family 036Algebraic and complex geometryNo LeanNot yet digested
Numerical semiampleness and generalized minimal models
Proves numerical semiampleness for nef adjoints with pseudo-effective and M nef rational, for projective klt rational pairs over algebraically closed characteristic-zero fields and smooth compact Kähler rational klt simple-normal-crossing pairs, using Bott–Chern cohomology in the latter case. Separately, projective generalized log canonical rational pairs over such fields admit minimal models for pseudo-effective adjoints and Mori fiber spaces otherwise, with nef b-data fixed.
Manuscripts in this family · 4
Numerical semiampleness of nef adjoint classes on compact Kähler manifolds
Oct 6, 2026·numerical-generalized-abundance.pdf
Let X be a smooth connected compact Kähler manifold, let B be an effective rational simple normal crossing divisor with coefficients less than one, and let M be a nef rational holomorphic line bundle on X. If is pseudo-effective and is nef, we prove that its first Chern class in real Bott–Chern cohomology is represented by a semiample rational line bundle. This numerical statement allows a flat change of line bundle; it does not assert semiampleness of the original adjoint.
Numerical Semiampleness of Nef Adjoint Divisors
Oct 3, 2026·paper.pdf
We prove the Generalised Abundance Conjecture: if is a projective klt ℚ-pair over an algebraically closed field of characteristic zero, is pseudo-effective, M is a nef ℚ-Cartier divisor on X, and is nef, then is numerically equivalent to a semiample ℚ-Cartier divisor on X.
Minimal models and Mori fibre spaces for generalized log canonical Q-pairs
Sep 24, 2026·paper.pdf
We resolve the existence form of the minimal-model conjecture for projective generalized log canonical ℚ-pairs over algebraically closed fields of characteristic zero. Such a pair admits a minimal model when its adjoint divisor is pseudo-effective, and a Mori fibre space otherwise, while keeping the nef ℚ-Cartier b-divisor fixed. Taking the nef part to be zero gives the corresponding result for ordinary log canonical ℚ-pairs.
Minimal models in numerical dimension one
Sep 24, 2026·paper.pdf
We resolve the numerical-dimension-one case of the minimal-model conjecture for smooth connected complex projective varieties of dimension at least three. If K is pseudo-effective and , with κ defined by section growth with a fixed ample twist, then X admits a projective ℚ-factorial terminal minimal model.