Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.10082 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917651849150464 |
|---|---|
| author | Koreeda, Yoshimune |
| author_facet | Koreeda, Yoshimune |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_10082 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Jet schemes of singular surfaces of types $D_4^0$ and $D_4^1$ in characteristic $2$ Koreeda, Yoshimune Algebraic Geometry 14J17 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. |
| title | Jet schemes of singular surfaces of types $D_4^0$ and $D_4^1$ in characteristic $2$ |
| topic | Algebraic Geometry 14J17 |
| url | https://arxiv.org/abs/2210.10082 |