Local vanishing for toric varieties
| Autor: | Shen, Wanchun, Venkatesh, Sridhar, Vo, Anh Duc |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00229-024-01553-3 |
| Popis: | Let $X$ be a toric variety. We establish vanishing (and non-vanishing) results for the sheaves $R^if_*\Omega^p_{\tilde X}(\log E)$, 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]. Comment: 17 pages; v2: Minor changes, following the referee's comments; to appear in manuscripta mathematica |
| Databáze: | arXiv |
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