Multiplier ideals and klt singularities via (derived) splittings
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866908877261373440 |
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| author | McDonald, Peter M. |
| author_facet | McDonald, Peter M. |
| contents | Let $X$ be a normal, excellent, noetherian scheme over $\operatorname{Spec}\mathbb{Q}$ with a dualizing complex. In this note, we find an alternate characterization of the multiplier ideal of $X$, as defined by de Fernex-Hacon, by considering maps $π_*ω_Y\to\mathcal{O}_X$ where $π:Y\to X$ ranges over all regular alterations. As a corollary to this result, we give a derived splinter characterization of klt singularities, akin to the characterization of rational singularities given by Kovács and Bhatt. We also give an analogous description of the test ideal in characteristic $p>2$ as a corollary to a result of Epstein-Schwede. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07906 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multiplier ideals and klt singularities via (derived) splittings McDonald, Peter M. Algebraic Geometry Commutative Algebra 14F18, 14B05, 14E15, 13A35 Let $X$ be a normal, excellent, noetherian scheme over $\operatorname{Spec}\mathbb{Q}$ with a dualizing complex. In this note, we find an alternate characterization of the multiplier ideal of $X$, as defined by de Fernex-Hacon, by considering maps $π_*ω_Y\to\mathcal{O}_X$ where $π:Y\to X$ ranges over all regular alterations. As a corollary to this result, we give a derived splinter characterization of klt singularities, akin to the characterization of rational singularities given by Kovács and Bhatt. We also give an analogous description of the test ideal in characteristic $p>2$ as a corollary to a result of Epstein-Schwede. |
| title | Multiplier ideals and klt singularities via (derived) splittings |
| topic | Algebraic Geometry Commutative Algebra 14F18, 14B05, 14E15, 13A35 |
| url | https://arxiv.org/abs/2307.07906 |