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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/2401.00677 |
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| _version_ | 1866910285246234624 |
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| author | Li, Yanjie Zhang, Shizhuo |
| author_facet | Li, Yanjie Zhang, Shizhuo |
| contents | Let $Q_i(i=1,2)$ be $2g$ dimensional quadrics in $\mathbb{P}^{2g+1}$ and let $Y$ be the smooth intersection $Q_1\cap Q_2$. We associate the linear subspace in $Y$ with vector bundles on the hyperelliptic curve $C$ of genus $g$ by the left adjoint functor of $Φ:D^b(C)\rightarrow D^b(Y)$. As an application, we give a different proof of the classification of line bundles and stable bundles of rank $2$ on hyperelliptic curves given by Desale and Ramanan. When $g=3$, we show that the projection functor induces a closed embedding $α:Y\rightarrow SU^s_C(4,h)$ into the moduli space of stable bundles on $C$ of rank $4$ of fixed determinant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00677 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear subspaces of the intersection of two quadrics via Kuznetsov component Li, Yanjie Zhang, Shizhuo Algebraic Geometry Let $Q_i(i=1,2)$ be $2g$ dimensional quadrics in $\mathbb{P}^{2g+1}$ and let $Y$ be the smooth intersection $Q_1\cap Q_2$. We associate the linear subspace in $Y$ with vector bundles on the hyperelliptic curve $C$ of genus $g$ by the left adjoint functor of $Φ:D^b(C)\rightarrow D^b(Y)$. As an application, we give a different proof of the classification of line bundles and stable bundles of rank $2$ on hyperelliptic curves given by Desale and Ramanan. When $g=3$, we show that the projection functor induces a closed embedding $α:Y\rightarrow SU^s_C(4,h)$ into the moduli space of stable bundles on $C$ of rank $4$ of fixed determinant. |
| title | Linear subspaces of the intersection of two quadrics via Kuznetsov component |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2401.00677 |