Abstract
We study local automorphisms of holomorphic Cartan geometries. This leads to classification results for compact complex manifolds admitting holomorphic Cartan geometries. We prove that a compact Kähler Calabi–Yau manifold bearing a holomorphic Cartan geometry of algebraic type admits a finite unramified cover which is a complex torus.
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Communicated by A. Cap.
This work was partially supported by the ANR Grant Symplexe BLAN 06-3-137237.
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Dumitrescu, S. Killing fields of holomorphic Cartan geometries. Monatsh Math 161, 145–154 (2010). https://doi.org/10.1007/s00605-009-0135-x
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DOI: https://doi.org/10.1007/s00605-009-0135-x