论文标题
格拉斯曼歧管的规范爆炸
Canonical blow-ups of Grassmann manifolds
论文作者
论文摘要
我们介绍了某些规范的爆炸$ \ MATHCAL T_ {s，p，n} $，以及它们独特的submanifolds $ \ Mathcal m_ {s，p，n} $，是Grassmann歧管$ g（p，n）$的$ g（p，n）$，通过对plückercoordination进行分区，以plückercoordination对parameTials进行分区。 Various geometric aspects of $\mathcal T_{s,p,n}$ and $\mathcal M_{s,p,n}$ are studied, for instance, the smoothness, the holomorphic symmetries, the (semi-)positivity of the anti-canonical bundles, the existence of Kähler-Einstein metrics, the functoriality, etc. In particular, we introduce the notion of $ \ Mathcal t_ {s，p，n} $的homeward cartactification是示例，作为奇妙的紧凑型的概括。最后，给出了$ \ Mathcal t_ {s，p，n} $根据向量值参数$ \ overline s $的概括，并提出了开放问题。
We introduce certain canonical blow-ups $\mathcal T_{s,p,n}$, as well as their distinct submanifolds $\mathcal M_{s,p,n}$, of Grassmann manifolds $G(p,n)$ by partitioning the Plücker coordinates with respect to a parameter $s$. Various geometric aspects of $\mathcal T_{s,p,n}$ and $\mathcal M_{s,p,n}$ are studied, for instance, the smoothness, the holomorphic symmetries, the (semi-)positivity of the anti-canonical bundles, the existence of Kähler-Einstein metrics, the functoriality, etc. In particular, we introduce the notion of homeward compactification, of which $\mathcal T_{s,p,n}$ are examples, as a generalization of the wonderful compactification. Lastly, a generalization of $\mathcal T_{s,p,n}$ according to vector-valued parameters $\overline s$ is given, and open questions are raised.
