Castelnuovo-Mumford regularity of finite schemes
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929641764159488 |
|---|---|
| author | Lee, Donghyeop Park, Euisung |
| author_facet | Lee, Donghyeop Park, Euisung |
| contents | Let $Γ\subset \mathbb{P}^n$ be a nondegenerate finite subscheme of degree $d$. Then the Castelnuovo-Mumford regularity ${\rm reg} (Γ)$ of $Γ$ is at most $\left\lceil \frac{d-n-1}{t(Γ)} \right\rceil +2$ where $t(Γ)$ is the smallest integer such that $Γ$ admits a $(t+2)$-secant $t$-plane. In this paper, we show that ${\rm reg} (Γ)$ is close to this upper bound if and only if there exists a unique rational normal curve $C$ of degree $t(Γ)$ such that ${\rm reg} (Γ\cap C) = {\rm reg} (Γ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15096 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Castelnuovo-Mumford regularity of finite schemes Lee, Donghyeop Park, Euisung Algebraic Geometry 14N25 Let $Γ\subset \mathbb{P}^n$ be a nondegenerate finite subscheme of degree $d$. Then the Castelnuovo-Mumford regularity ${\rm reg} (Γ)$ of $Γ$ is at most $\left\lceil \frac{d-n-1}{t(Γ)} \right\rceil +2$ where $t(Γ)$ is the smallest integer such that $Γ$ admits a $(t+2)$-secant $t$-plane. In this paper, we show that ${\rm reg} (Γ)$ is close to this upper bound if and only if there exists a unique rational normal curve $C$ of degree $t(Γ)$ such that ${\rm reg} (Γ\cap C) = {\rm reg} (Γ)$. |
| title | Castelnuovo-Mumford regularity of finite schemes |
| topic | Algebraic Geometry 14N25 |
| url | https://arxiv.org/abs/2412.15096 |