Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: Family 051. Kobayashi's canonical-ampleness conjecture
Family claims › Algebraic and complex geometry · lines 488–493
OpenAI@2026-10-07#rem:oai-051
Every compact connected Kähler manifold of positive complex dimension with no nonconstant entire curve has ample canonical bundle and is therefore projective. This proves Kobayashi's canonical-ampleness conjecture in the smooth compact Kähler setting.
The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- remark: Remark: Family 032. The rational Hodge conjecture for CM abelian varieties
- remark: Remark: Family 033. Campana's orbifold Iitaka conjecture and logarithmic subadditivity
- remark: Remark: Family 034. Log abundance and effective Iitaka fibrations
- remark: Remark: Family 035. Threefold log abundance in numerical dimension one in characteristic p>3
- remark: Remark: Family 036. Numerical semiampleness and generalized minimal models
- remark: Remark: Family 037. The sharp ordinary-double-point volume gap
- remark: Remark: Family 038. Fujita's freeness conjecture
- remark: Remark: Family 039. Nagata's conjecture and maximal Seshadri constants