Stable Reduction via the Log Canonical Model
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913587295944704 |
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| author | Chung, Tai-Hsuan |
| author_facet | Chung, Tai-Hsuan |
| contents | We formulate a stable reduction conjecture that extends Deligne-Mumford's stable reduction to higher dimensions and provide a simple proof that it holds in large characteristic, assuming two standard conjectures of the Minimal Model Program. As a result, we recover the Hacon-Kovács theorem on the properness of the moduli stack $\overline{\mathscr{M}}_{2,v,k}$ of stable surfaces of volume $v$ defined over $k=\overline{k}$, provided that $\operatorname{char}k>C(v)$, a constant depending only on $v$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17909 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stable Reduction via the Log Canonical Model Chung, Tai-Hsuan Algebraic Geometry 14D06, 14E30, 14G17, 14J17 We formulate a stable reduction conjecture that extends Deligne-Mumford's stable reduction to higher dimensions and provide a simple proof that it holds in large characteristic, assuming two standard conjectures of the Minimal Model Program. As a result, we recover the Hacon-Kovács theorem on the properness of the moduli stack $\overline{\mathscr{M}}_{2,v,k}$ of stable surfaces of volume $v$ defined over $k=\overline{k}$, provided that $\operatorname{char}k>C(v)$, a constant depending only on $v$. |
| title | Stable Reduction via the Log Canonical Model |
| topic | Algebraic Geometry 14D06, 14E30, 14G17, 14J17 |
| url | https://arxiv.org/abs/2411.17909 |