Threefolds containing all curves are rationally connected
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912072539832320 |
|---|---|
| author | Lou, Sixuan |
| author_facet | Lou, Sixuan |
| contents | Any smooth projective curve embeds into $\mathbb{P}^3$. More generally, any curve embeds into a rationally connected variety of dimension at least three. We prove conversely that if every curve embeds in a threefold $X$, then $X$ is rationally connected. In particular "all curves embed" is a birational property for threefolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10656 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Threefolds containing all curves are rationally connected Lou, Sixuan Algebraic Geometry Any smooth projective curve embeds into $\mathbb{P}^3$. More generally, any curve embeds into a rationally connected variety of dimension at least three. We prove conversely that if every curve embeds in a threefold $X$, then $X$ is rationally connected. In particular "all curves embed" is a birational property for threefolds. |
| title | Threefolds containing all curves are rationally connected |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2410.10656 |