论文标题
川玛塔原木终端的全等级
Kawamata log terminal singularities of full rank
论文作者
论文摘要
我们研究了全等级的kawamata日志终端奇异性，即$ n $二维的吉隆坡奇异性，其中包含大量有限的Abelian Rank $ n $组成的区域基本组。本文的主要结果是，在对数毛皮的等效复合品品种上，全等级的KLT奇异性是圆锥的。为了建立主要定理，我们将证明的证明减少到对具有全等级有限的自动形态的Fano类型品种的研究。我们证明，这种Fano类型的品种是对数毛po的等效复合物。此外，任何这样的fano dimension $ n $都包含一个开放式仿射子集同构为$ \ mathbb {g} _m^n $。作为第一个应用程序，我们研究了全等级的KLT奇异性的补充。作为第二次应用，我们研究了具有大量基本基因座的Fano类型品种上的对数Calabi-yau结构的双重复合物。
We study Kawamata log terminal singularities of full rank, i.e., $n$-dimensional klt singularities containing a large finite abelian group of rank $n$ in its regional fundamental group. The main result of this article is that klt singularities of full rank degenerate to cones over log crepant equivalent toric quotient varieties. To establish the main theorem, we reduce the proof to the study of Fano type varieties with large finite automorphisms of full rank. We prove that such Fano type varieties are log crepant equivalent toric. Furthermore, any such Fano variety of dimension $n$ contains an open affine subset isomorphic to $\mathbb{G}_m^n$. As a first application, we study complements on klt singularities of full rank. As a second application, we study dual complexes of log Calabi-Yau structures on Fano type varieties with large fundamental group of their smooth locus.
