{"id":"openai-math/Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds","pdf":"https://github.com/openai/math/blob/main/preprints/Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026/canonical-ampleness.pdf","url":"https://github.com/openai/math/tree/main/preprints/Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026","tags":["kahler-geometry","hyperbolic-manifolds","algebraic-geometry"],"score":0,"title":"Canonical ampleness of compact hyperbolic Kähler manifolds","domain":"Algebraic and complex geometry","family":"051","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Kobayashi’s canonical-ampleness conjecture"}