Local vanishing for toric varieties
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909183320784896 |
|---|---|
| author | Shen, Wanchun Venkatesh, Sridhar Vo, Anh Duc |
| author_facet | Shen, Wanchun Venkatesh, Sridhar Vo, Anh Duc |
| contents | Let $X$ be a toric variety. We establish vanishing (and non-vanishing) results for the sheaves $R^if_*Ω^p_{\tilde X}(\log E)$, where $f: \tilde{X} \to X$ is a strong log resolution of singularities with reduced exceptional divisor $E$. These extend the local vanishing theorem for toric varieties in [MOP20]. Our consideration of these sheaves is motivated by the notion of $k$-rational singularities introduced by Friedman and Laza [FL22b]. In particular, our results lead to criteria for toric varieties to have $k$-rational singularities, as defined in [SVV23]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10179 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Local vanishing for toric varieties Shen, Wanchun Venkatesh, Sridhar Vo, Anh Duc Algebraic Geometry Commutative Algebra 14M25, 14F17, 14B05 Let $X$ be a toric variety. We establish vanishing (and non-vanishing) results for the sheaves $R^if_*Ω^p_{\tilde X}(\log E)$, where $f: \tilde{X} \to X$ is a strong log resolution of singularities with reduced exceptional divisor $E$. These extend the local vanishing theorem for toric varieties in [MOP20]. Our consideration of these sheaves is motivated by the notion of $k$-rational singularities introduced by Friedman and Laza [FL22b]. In particular, our results lead to criteria for toric varieties to have $k$-rational singularities, as defined in [SVV23]. |
| title | Local vanishing for toric varieties |
| topic | Algebraic Geometry Commutative Algebra 14M25, 14F17, 14B05 |
| url | https://arxiv.org/abs/2306.10179 |