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Complex Manifolds

Ed. by Fino, Anna Maria

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Holomorphic Cartan geometries and rational curves

Indranil Biswas / Benjamin McKay
Published Online: 2016-03-21 | DOI: https://doi.org/10.1515/coma-2016-0004


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.

MSC: 53C55; 53C51; 53C56; 53A55


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About the article

Received: 2015-10-30

Accepted: 2016-02-25

Published Online: 2016-03-21

Citation Information: Complex Manifolds, Volume 3, Issue 1, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2016-0004.

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© 2016 Indranil Biswas and Benjamin McKay. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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