论文标题
关于$ \ mathbb {q} $的分类 - gorenstein Index 2.iii的Fano 3倍
On Classification of $\mathbb{Q}$-Fano 3-folds of Gorenstein index 2. III
论文作者
论文摘要
我们对Prime $ \ Mathbb {Q} $ - Fano $ 3 $ -folds $ x $，只有$ 1/2（1,1,1）$ - 奇异性，$ h^{0}（-k_ {x}）分类是通过以$ 1/2（1,1,1）$ - 奇异性并构建sarkisov链接来炸毁每个$ x $。本文的目的是揭示Sarkisov链接背后的几何形状，价格为5堂。主要结果断言，这5个类中的任何$ x $都可以嵌入为线性部分中的较大尺寸$ \ mathbb {q} $ - fano品种称为钥匙品种，其中密钥品种是通过在较高尺寸中部分扩展sarkisov链接来构建的。
We classified prime $\mathbb{Q}$-Fano $3$-folds $X$ with only $1/2(1,1,1)$-singularities and with $h^{0}(-K_{X})\geq 4$ a long time ago. The classification was undertaken by blowing up each $X$ at one $1/2(1,1,1)$-singularity and constructing a Sarkisov link. The purpose of this paper is to reveal the geometries behind the Sarkisov links for $X$ in 5 classes. The main result asserts that any $X$ in the 5 classes can be embedded as linear sections into bigger dimensional $\mathbb{Q}$-Fano varieties called key varieties, where the key varieties are constructed by extending partially the Sarkisov link in higher dimensions.
