论文标题
用nef抗民主分裂的投射品种的结构：对数末端奇点的情况
Structure of projective varieties with nef anticanonical divisor: the case of log terminal singularities
论文作者
论文摘要
在本文中，我们研究了KLT射击抗性分裂的klt投射品种的结构（更普遍地，是半法诺类型的品种），尤其是与之相关的规范纤维。我们表明：1。这种品种的Albanese地图是一种局部恒定的纤维化（即带有连接的纤维的分析纤维束，$ x $等于阿尔巴内斯地图商的纤维通过Albanese torus的基本肌的对角线作用，是阿尔巴尼斯地图商的通用覆盖物的产物）； 2。如果平滑的基因座是简单地连接的，则这种品种的MRC纤维纤维是到处定义的形态，并诱导分解为合理连接的品种和具有微不足道的典型分裂的投射品种的产物。这些将CAO（2019）和Cao-Höring（2019）中的Nef反典型捆绑的光滑投射品种的相应结果推广到KLT案例，也可以被视为奇异的Beauville-Bogomolov分解理论的部分扩展，这是由Greb-Keb-kebebekus-Peternell（2016）（2016）（2016），drielem（2016），driel（2016），（2016），（2016）寻找壁式 - 格雷布·基比克斯（2019）和霍林·彼得内尔（Höring-Peternell）（2019）。
In this article we study the structure of klt projective varieties with nef anticanonical divisor (and more generally, varieties of semi-Fano type), especially the canonical fibrations associated to them. We show that: 1. the Albanese map for such variety is a locally constant fibration (that is, an analytic fibre bundle with connected fibres that $X$ is equal to the product of the universal cover of the Albanese torus by the fibre of the Albanese map quotient by a diagonal action of the fundamenatl group of the Albanese torus); 2. if the smooth locus is simply connected, the MRC fibration of such variety is an everywhere defined morphism and induces a decomposition into a product of a rationally connected variety and of a projective variety with trivial canonical divisor. These generalize the corresponding results for smooth projective varieties with nef anticanonical bundle in Cao (2019) and Cao-Höring (2019) to the klt case, and can be also regarded as a partial extension of the singular Beauville-Bogomolov decomposition theorem proved by successive works of Greb-Kebekus-Peternell (2016), Druel (2018), Guenencia-Greb-Kebekus (2019) and Höring-Peternell (2019).
