Infinitesimal structure of log canonical thresholds
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866914825752281088 |
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| author | Liu, Jihao Meng, Fanjun Xie, Lingyao |
| author_facet | Liu, Jihao Meng, Fanjun Xie, Lingyao |
| contents | We show that log canonical thresholds of fixed dimension are standardized. More precisely, we show that any sequence of log canonical thresholds in fixed dimension $d$ accumulates in a way which is i) either similar to how standard and hyperstandard sets accumulate, or ii) to log canonical thresholds in dimension $\leq d-2$. This provides an accurate description on the infinitesimal structure of the set of log canonical thresholds. We also discuss similar behaviors of minimal log discrepancies, canonical thresholds, and K-semistable thresholds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_11369 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Infinitesimal structure of log canonical thresholds Liu, Jihao Meng, Fanjun Xie, Lingyao Algebraic Geometry 14E30, 14B05 We show that log canonical thresholds of fixed dimension are standardized. More precisely, we show that any sequence of log canonical thresholds in fixed dimension $d$ accumulates in a way which is i) either similar to how standard and hyperstandard sets accumulate, or ii) to log canonical thresholds in dimension $\leq d-2$. This provides an accurate description on the infinitesimal structure of the set of log canonical thresholds. We also discuss similar behaviors of minimal log discrepancies, canonical thresholds, and K-semistable thresholds. |
| title | Infinitesimal structure of log canonical thresholds |
| topic | Algebraic Geometry 14E30, 14B05 |
| url | https://arxiv.org/abs/2209.11369 |