The tilting property for $F_*^e\mathcal O_X$ on Fano surfaces and threefolds
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_ | 1866908573920919552 |
|---|---|
| author | Mallory, Devlin |
| author_facet | Mallory, Devlin |
| contents | Let $X$ be a smooth variety over a field of characteristic $p$. It is a natural question whether the Frobenius pushforwards $F_*^e\mathcal O_X$ of the structure sheaf are tilting bundles. We show if $X$ is a smooth del Pezzo surface of degree $\leq 3$ or a Fano threefold with $\mathrm{vol}(K_X)<24$ over a field of characteristic $p$, then $\mathrm{Ext}^i(F_*^e\mathcal O_X,F^e_*\mathcal O_X)\neq 0$ and thus $F_*^e\mathcal O_X$ is not tilting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14070 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The tilting property for $F_*^e\mathcal O_X$ on Fano surfaces and threefolds Mallory, Devlin Algebraic Geometry Commutative Algebra Let $X$ be a smooth variety over a field of characteristic $p$. It is a natural question whether the Frobenius pushforwards $F_*^e\mathcal O_X$ of the structure sheaf are tilting bundles. We show if $X$ is a smooth del Pezzo surface of degree $\leq 3$ or a Fano threefold with $\mathrm{vol}(K_X)<24$ over a field of characteristic $p$, then $\mathrm{Ext}^i(F_*^e\mathcal O_X,F^e_*\mathcal O_X)\neq 0$ and thus $F_*^e\mathcal O_X$ is not tilting. |
| title | The tilting property for $F_*^e\mathcal O_X$ on Fano surfaces and threefolds |
| topic | Algebraic Geometry Commutative Algebra |
| url | https://arxiv.org/abs/2405.14070 |