论文标题
kähler歧管和混合曲率
Kähler manifolds and mixed curvature
论文作者
论文摘要
在这项工作中，我们考虑了具有非阳性混合曲率的紧凑型kähler歧管，这是Ricci曲率和全态截面曲率的“凸组合”。我们表明，在这种情况下，规范线束为nef。此外，如果曲率在某个时候为负，则歧管是投影的，规范线捆绑包大且nef。如果另外，曲率为负，则规范线束很丰富。作为应用程序，我们回答了一个关于带负$ K $ -RICCI曲率流形的NI问题，并将Wu-Yau和Diverio-Trapani的结果概括为保态kähler案。我们还表明，紧凑型kähler歧管是投影性的，如果混合曲率为正，则仅连接。
In this work we consider compact Kähler manifolds with non-positive mixed curvature which is a "convex combination" of Ricci curvature and holomorphic sectional curvature. We show that in this case, the canonical line bundle is nef. Moreover, if the curvature is negative at some point, then the manifold is projective with canonical line bundle being big and nef. If in addition the curvature is negative, then the canonical line bundle is ample. As an application, we answer a question of Ni concerning manifolds with negative $k$-Ricci curvature and generalize a result of Wu-Yau and Diverio-Trapani to the conformally Kähler case. We also show that the compact Kähler manifold is projective and simply connected if the mixed curvature is positive.
