Terminal 3-folds that are not Cohen-Macaulay
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929466538721280 |
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| author | Totaro, Burt |
| author_facet | Totaro, Burt |
| contents | An important local vanishing theorem for the minimal model program is the fact that klt singularities in characteristic zero are Cohen-Macaulay. In contrast, even in the narrow setting of terminal singularities of dimension 3, we show that Cohen-Macaulayness can fail in characteristic $p$ or mixed characteristic $(0,p)$ for $p$ equal to 2, 3, or 5. This is optimal, by work of Arvidsson-Bernasconi-Lacini.
The examples are quotients of regular schemes by the cyclic group $G$ of order $p$. In characteristic $p$ or mixed characteristic, such quotients can exhibit a wide range of behavior. Our key technical tool is a sufficient condition for quotients by $G$ to have only toric singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02608 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Terminal 3-folds that are not Cohen-Macaulay Totaro, Burt Algebraic Geometry Commutative Algebra 14G17 (Primary) 13A50, 14F17, 14J17 (Secondary) An important local vanishing theorem for the minimal model program is the fact that klt singularities in characteristic zero are Cohen-Macaulay. In contrast, even in the narrow setting of terminal singularities of dimension 3, we show that Cohen-Macaulayness can fail in characteristic $p$ or mixed characteristic $(0,p)$ for $p$ equal to 2, 3, or 5. This is optimal, by work of Arvidsson-Bernasconi-Lacini. The examples are quotients of regular schemes by the cyclic group $G$ of order $p$. In characteristic $p$ or mixed characteristic, such quotients can exhibit a wide range of behavior. Our key technical tool is a sufficient condition for quotients by $G$ to have only toric singularities. |
| title | Terminal 3-folds that are not Cohen-Macaulay |
| topic | Algebraic Geometry Commutative Algebra 14G17 (Primary) 13A50, 14F17, 14J17 (Secondary) |
| url | https://arxiv.org/abs/2407.02608 |