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- W3100389196 abstract "Let X be a compact connected Kaehler manifold such that the holomorphic tangent bundle TX is numerically effective. A theorem of Demailly, Peternell and Schenider says that there is a finite unramified Galois covering M --> X, a complex torus T, and a holomorphic surjective submersion f: M --> T, such that the fibers of f are Fano manifolds with numerically effective tangent bundle. A conjecture of Campana and Peternell says that the fibers of f are rational and homogeneous. Assume that X admits a holomorphic Cartan geometry. We prove that the fibers of f are rational homogeneous varieties. We also prove that the holomorphic principal G-bundle over T given by f, where G is the group of all holomorphic automorphisms of a fiber, admits a flat holomorphic connection." @default.
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- W3100389196 date "2011-03-01" @default.
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- W3100389196 title "Holomorphic Cartan geometry on manifolds with numerically effective tangent bundle" @default.
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- W3100389196 doi "https://doi.org/10.1016/j.difgeo.2011.02.001" @default.
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