A remark on some punctual Quot schemes on smooth projective curves
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908362891853824 |
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| author | Ito, Atsushi |
| author_facet | Ito, Atsushi |
| contents | For a locally free sheaf $\mathcal{E}$ on a smooth projective curve, we can define the punctual Quot scheme which parametrizes torsion quotients of $\mathcal{E}$ of length $n$ supported at a fixed point. It is known that the punctual Quot scheme is a normal projective variety with canonical Gorenstein singularities. In this note, we show that the punctual Quot scheme is a $\mathbb{Q}$-factorial Fano variety of Picard number one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01335 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A remark on some punctual Quot schemes on smooth projective curves Ito, Atsushi Algebraic Geometry For a locally free sheaf $\mathcal{E}$ on a smooth projective curve, we can define the punctual Quot scheme which parametrizes torsion quotients of $\mathcal{E}$ of length $n$ supported at a fixed point. It is known that the punctual Quot scheme is a normal projective variety with canonical Gorenstein singularities. In this note, we show that the punctual Quot scheme is a $\mathbb{Q}$-factorial Fano variety of Picard number one. |
| title | A remark on some punctual Quot schemes on smooth projective curves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2504.01335 |