Classification of Toric Manifolds over an n-Cube with One Vertex Cut
Classification of Toric Manifolds over an n-Cube with One Vertex Cut
复制标题
具有一个顶点切割的 n 立方体上的环面流形的分类
DOI：
10.1093/imrn/rny161
复制
发表时间：
2018
影响因子：
1
通讯作者：
Seonjeong Park
中科院分区：
文献类型：
--
作者：
Sho Hasui;Hideya Kuwata;Mikiya Masuda;Seonjeong Park
一个完备的非奇异环面簇（称为环面流形）是覆盖的，如果它与紧环面的商同胚于一个带角点的流形。Bott流形是一个立方体上的环面流形，在一个固定点上将它们爆破，得到一个立方体上的环面流形，有一个顶点切割。它们都是投射的。另一方面，织田的三重，最简单的非投射环面流形，结束了。本文将环曲面流形分类为簇和光滑流形.结果表明，环上存在许多非投射环面流形，但它们都是复纯的，并且在某些类中，环上的环面流形由它们的上同调环作为簇来确定。
A complete nonsingular toric variety (called a toric manifold) is overif its quotient by the compact torus is homeomorphic toas a manifold with corners. Bott manifolds are toric manifolds over an-cubeand blowing them up at a fixed point produces toric manifolds overan-cube with one vertex cut. They are all projective. On the other hand, Oda’s three-fold, the simplest non-projective toric manifold, is over. In this paper, we classify toric manifolds overas varieties and as smooth manifolds. It consequently turns out that there are many non-projective toric manifolds overbut they are all diffeomorphic, and toric manifolds overin some class are determined by their cohomology rings as varieties.