Holomorphic Cartan geometries and rational curves

Details Holomorphic Cartan geometries and rational curves Holomorphic Cartan geometries and rational curves

2010-05-10

arxiv.org/abs/1005.1472v3

Mathematics

Differential Geometry

38 pages, 0 figures

Scientific paper

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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