Canonical ampleness of compact hyperbolic Kähler manifolds
We prove that every compact connected Kähler manifold of positive complex dimension containing no nonconstant entire curve has ample canonical bundle and is projective. This resolves positively Kobayashi's canonical-ampleness conjecture in the smooth compact Kähler category.
Cite
@misc{OAI:Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026,
author = {{OpenAI}},
title = {{Canonical ampleness of compact hyperbolic K{\"a}hler manifolds}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026/canonical-ampleness.pdf}{OAI:Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026}},
year = {2026}
}