We prove that any compact Kähler 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 Kähler manifold. This shows that many complex manifolds admit no or few holomorphic Cartan geometries.
@article{bwmeta1.element.doi-10_1515_coma-2016-0004,
author = {Indranil Biswas and Benjamin McKay},
title = {Holomorphic Cartan geometries and rational curves},
journal = {Complex Manifolds},
volume = {3},
year = {2016},
zbl = {1341.53107},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_coma-2016-0004}
}
Indranil Biswas; Benjamin McKay. Holomorphic Cartan geometries and rational curves. Complex Manifolds, Tome 3 (2016) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_coma-2016-0004/