发表机构
The University of Sydney（悉尼大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用Kähler-Ricci流重新证明Miyaoka-Yau不等式与斜率半稳定性，并揭示半丰沛典范线丛情形下Miyaoka-Yau量等于Weil-Petersson与Fubini-Study度量相交，等号条件为多重典范映射成为全纯纤维丛。
AI 中文摘要
我们利用Kähler-Ricci流为若干已知的Miyaoka-Yau不等式和斜率半稳定性给出替代证明，特别是针对具有半丰沛典范线丛的紧Kähler流形和K-半稳定的Fano流形。此外，当典范线丛半丰沛且Kodaira维数为$n-1$时，我们证明Miyaoka-Yau量等于典范模型上Weil-Petersson度量与Fubini-Study度量的相交数。因此，Miyaoka-Yau不等式中等号成立当且仅当多重典范映射是全纯纤维丛。
英文摘要
We use the Kähler-Ricci flow to give alternate proofs of several known Miyaoka-Yau inequalities and slope semi-stabilities, in particular, for the case of compact Kähler manifolds with semi-ample canonical line bundles and K-semistable Fano manifolds. Moreover, when the canonical line bundle is semi-ample, and the Kodaira dimension is $n-1$, we prove the Miyaoka-Yau quantity is equal to the intersection of the Weil-Petersson metric and the Fubini-Study metric on the canonical model. Consequently, equality holds in the Miyaoka-Yau inequality if and only if the pluricanonical map is a holomorphic fibre bundle.
Comments24 pages
