Holomorphic Cartan geometries and rational curves
classification
🧮 math.DG
math.AG
keywords
cartangeometryholomorphicahlercompactmanifoldrationalbearing
read the original abstract
We prove that any compact K\"ahler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact K\"ahler manifold.
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