论文标题
类型$ d_4^0 $和$ d_4^1 $ in特征$ 2 $的奇异表面的喷气计划
Jet schemes of singular surfaces of types $D_4^0$ and $D_4^1$ in characteristic $2$
论文作者
论文摘要
让$ k $成为一个代数关闭的字段，$ s $ a a + $ k $的$ s $ a a $ k $和m a非负整数。 $ S $上有一个$ s_m $，称为$ m $ $ x $的JET计划，参数化$ m $ $ th $ th $ s $。 $ s $的单数基因座上的纤维称为单数纤维。在本文中，我们考虑了二维合理双点的奇异纤维在特征性$ 2 $的场$ k $上，其分辨率图的分辨率为$ d_4 $。这种奇异性有两种类型，类型为$ d_4^0 $和类型$ d_4^1 $。我们给出奇异纤维的不可还原分解，并描述不可约组件的构型。 $ d_4^0 $ - 单位性的情况与[3]中研究的特征$ 0 $的情况非常相似。 $ d_4^1 $ - 单一性的情况需要对单数纤维的某些子集进行更精细的分析。
Let $k$ be an algebraically closed field, $S$ a variety over $k$ and m a nonnegative integer. There is a space $S_m$ over $S$ , called the jet scheme of $X$ of order $m$, parameterizing $m$-th jets on $S$. The fiber over the singular locus of $S$ is called the singular fiber. In this paper, we consider the singular fibers of the jet schemes of 2-dimensional rational double points over a field $k$ of characteristic $2$ whose resolution graph is of type $D_4$. There are two types of such singularities, of type $D_4^0$ and type $D_4^1$. We give the irreducible decomposition of the singular fiber and describe the configuration of the irreducible components. The case of a $D_4^0$-singularity is quite similar to the case of characteristic $0$ studied in [3]. The case of $D_4^1$-singularity requires more elaborate analysis of certain subsets of the singular fiber.
