论文标题
复曲面上的奇异性
Singularities on toric fibrations
论文作者
论文摘要
在本文中，我们研究了关于曲曲面纤维的奇异性。在这种情况下，我们研究了shokurov的猜想（其中一种特殊情况是由于m $^\ rm {c} $ kernan引起的），大致说，如果$（x，b）\ z $是$（x，b）\ to z $是$ε$ -lc fano type log log calabi-yau启动x $ when，$ b_z，m_z $是规范捆绑套件公式的判别和模量分隔线。我们的主要结果的推论说，如果$ x \ to z $是一种复式的fano纤维，$ x $为$ε$ -LC，则相对于$ε$和$ \ \ \ \ dim x $，纤维的多数纤维超过codimension。
In this paper we investigate singularities on toric fibrations. In this context we study a conjecture of Shokurov (a special case of which is due to M$^\rm{c}$Kernan) which roughly says that if $(X,B)\to Z$ is an $ε$-lc Fano type log Calabi-Yau fibration, then the singularities of the log base $(Z,B_Z+M_Z)$ are bounded in terms of $ε$ and $\dim X$ where $B_Z,M_Z$ are the discriminant and moduli divisors of the canonical bundle formula. A corollary of our main result says that if $X\to Z$ is a toric Fano fibration with $X$ being $ε$-lc, then the multiplicities of the fibres over codimension one points are bounded depending only on $ε$ and $\dim X$.
