Embeddings of weighted projective spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917292534661120 |
|---|---|
| author | Adeyemo, Praise Bunnett, Dominic Levicán-Santibáñez, Fabián |
| author_facet | Adeyemo, Praise Bunnett, Dominic Levicán-Santibáñez, Fabián |
| contents | Let $X$ be a projective toric variety of dimension $n$ and let $L$ be a ample line bundle on $X$. For $k \geq 0$, it is in general difficult to determine whether $L^{\otimes k}$ is very ample and whether it additionally gives a projectively normal embedding. These two properties are equivalent to the very ampleness, respectively normality, of the corresponding polytope. By a result of Ewald-Wessels, both statements are classically known to hold for $k \geq n - 1$.
We study embeddings of weighted projective spaces $\mathbb{P}(a_0, ..., a_n)$ via their corresponding rectangular simplices $Δ(λ_1, ..., λ_n)$. We give multiple criteria (depending on arithmetic properties of the weights $a_i$) to obtain bounds for the power $k$ which are sharp in many cases. We also introduce combinatorial tools that allow us to systematically construct families exhibiting extremal behaviour. These results extend earlier work of Payne, Hering and Bruns-Gubeladze. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05076 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Embeddings of weighted projective spaces Adeyemo, Praise Bunnett, Dominic Levicán-Santibáñez, Fabián Algebraic Geometry Combinatorics Let $X$ be a projective toric variety of dimension $n$ and let $L$ be a ample line bundle on $X$. For $k \geq 0$, it is in general difficult to determine whether $L^{\otimes k}$ is very ample and whether it additionally gives a projectively normal embedding. These two properties are equivalent to the very ampleness, respectively normality, of the corresponding polytope. By a result of Ewald-Wessels, both statements are classically known to hold for $k \geq n - 1$. We study embeddings of weighted projective spaces $\mathbb{P}(a_0, ..., a_n)$ via their corresponding rectangular simplices $Δ(λ_1, ..., λ_n)$. We give multiple criteria (depending on arithmetic properties of the weights $a_i$) to obtain bounds for the power $k$ which are sharp in many cases. We also introduce combinatorial tools that allow us to systematically construct families exhibiting extremal behaviour. These results extend earlier work of Payne, Hering and Bruns-Gubeladze. |
| title | Embeddings of weighted projective spaces |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2510.05076 |