Holomorphic Cartan geometries, Calabi--Yau manifolds and rational curves
Holomorphic Cartan geometries, Calabi--Yau manifolds and rational curves
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全纯嘉当几何、卡拉比-丘流形和有理曲线
DOI：
10.1016/j.difgeo.2009.09.003
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
B. McKay
中科院分区：
文献类型：
--
作者：
I. Biswas;B. McKay
我们证明了如果一个Calabi-Yau流形M允许一个全纯Cartan几何，则M被一个复环面覆盖。这是通过建立紧Kähler流形上半稳定层的Bogomolov不等式来完成的。我们还分类所有的全纯Cartan几何的有理连通复射影流形。
We prove that if a Calabi–Yau manifold M admits a holomorphic Cartan geometry, then M is covered by a complex torus. This is done by establishing the Bogomolov inequality for semistable sheaves on compact Kähler manifolds. We also classify all holomorphic Cartan geometries on rationally connected complex projective manifolds.