学术报告（方汉隆 1.18）

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. 
我们引入格拉斯曼流形G(p,n)的一些典范爆破T_{s,p,n}，及其子流形M_{s,p,n}，通过其普吕克坐标的相对于一个参数s的划分。我们研究了T_{s,p,n}和M_{s,p,n}的各种几何性质。例如，光滑性，全纯对称性，反典范丛的正性与半正性，凯勒-爱因斯坦度量的存在性，函子性等。特别的，我们以T_{s,p,n} 为例，引入“家向紧化”的概念，作为“奇妙紧化”的推广。