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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.05532 |
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| _version_ | 1866917364974485504 |
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| author | Rasul, Parvez Sebastian, Ronnie |
| author_facet | Rasul, Parvez Sebastian, Ronnie |
| contents | Let $C$ be a smooth projective curve over $\mathbb C$ of genus $g\geqslant 1$. Let $E$ be a vector bundle on $C$ of rank $r$ and degree $e$. Given integers $k_1,k_2,d_1,d_2$ such that $r>k_1>k_2>0$, let $\mathcal Q^{k_1,k_2}_{d_1,d_2}(E)$ denote the nested Quot scheme which parametrizes pair of quotients $[E \twoheadrightarrow F_1 \twoheadrightarrow F_2]$ such that $F_i$ has rank $k_i$ and degree $d_i$. We show that these nested Quot schemes are integral, local complete intersection schemes when $d_1\gg d_2\gg 0$ or $d_2\gg d_1\gg 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05532 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Irreducibility and singularities of some nested Quot schemes Rasul, Parvez Sebastian, Ronnie Algebraic Geometry 14H60 Let $C$ be a smooth projective curve over $\mathbb C$ of genus $g\geqslant 1$. Let $E$ be a vector bundle on $C$ of rank $r$ and degree $e$. Given integers $k_1,k_2,d_1,d_2$ such that $r>k_1>k_2>0$, let $\mathcal Q^{k_1,k_2}_{d_1,d_2}(E)$ denote the nested Quot scheme which parametrizes pair of quotients $[E \twoheadrightarrow F_1 \twoheadrightarrow F_2]$ such that $F_i$ has rank $k_i$ and degree $d_i$. We show that these nested Quot schemes are integral, local complete intersection schemes when $d_1\gg d_2\gg 0$ or $d_2\gg d_1\gg 0$. |
| title | Irreducibility and singularities of some nested Quot schemes |
| topic | Algebraic Geometry 14H60 |
| url | https://arxiv.org/abs/2404.05532 |