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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.16779 |
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| _version_ | 1866912381726097408 |
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| author | Qu, F. |
| author_facet | Qu, F. |
| contents | Let $X$ be a Deligne-Mumford stack locally of finite type over an algebraically closed field $k$ of characteristic zero. We show that the intrinsic normal cone $C_X$ of $X$ is supported in the subcone $\mathbb{V}(Ω_X[-1])$ ($h^1/h^0((Ω^1_X)^\vee)$) of its intrinsic normal sheaf $N_X$. This leads to an alternative proof of cone reduction by cosections for $C_X$. We also discuss vanishing of simple obstructions under the Buchweitz-Flenner semiregularity map for sheaves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16779 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simple obstructions and cone reduction Qu, F. Algebraic Geometry Let $X$ be a Deligne-Mumford stack locally of finite type over an algebraically closed field $k$ of characteristic zero. We show that the intrinsic normal cone $C_X$ of $X$ is supported in the subcone $\mathbb{V}(Ω_X[-1])$ ($h^1/h^0((Ω^1_X)^\vee)$) of its intrinsic normal sheaf $N_X$. This leads to an alternative proof of cone reduction by cosections for $C_X$. We also discuss vanishing of simple obstructions under the Buchweitz-Flenner semiregularity map for sheaves. |
| title | Simple obstructions and cone reduction |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2405.16779 |