Every positive-dimensional compact connected Kähler manifold with no nonconstant holomorphic map from the complex line has ample canonical bundle and is projective.
Every positive-dimensional compact connected Kähler manifold with no nonconstant holomorphic map from the complex line has ample canonical bundle and is projective.
Every positive-dimensional compact connected Kähler manifold with no nonconstant holomorphic map from the complex line has ample canonical bundle and is projective.
If correct, resolves Kobayashi’s canonical-ampleness conjecture in the smooth compact Kähler category.
Does absence of entire curves force the canonical bundle of a compact Kähler manifold to be ample?
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OpenAI reports canonical ampleness for compact hyperbolic Kähler manifolds
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