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Holomorphic Cartan geometries and rational curves

Published 10 May 2010 in math.DG and math.AG | (1005.1472v6)

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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