An Equisingular Specialisation of the Compactified Jacobian and its applications
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866917968806412288 |
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| author | Das, Sourav Parameswaran, A. J. Sarkar, Subham |
| author_facet | Das, Sourav Parameswaran, A. J. Sarkar, Subham |
| contents | For any positive integer $k$, let $X_k$ be a projective irreducible nodal curve with $k$ nodes. We show that the Betti numbers and the mixed Hodge numbers of the compactified Jacobian $\overline{J_{k}}$ of an irreducible nodal curve $X_k$ with $k$ nodes are the same as the Betti numbers and the mixed Hodge numbers of $J_0\times R^k$, where $J_0$ is the Jacobian of the normalisation of the irreducible nodal curve and $R$ denotes the rational nodal curve with one node. We prove it by constructing a topologically locally trivial family of projective varieties containing $\overline{J_{k}}$ and $J_0\times R^k$ as fibres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_12259 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | An Equisingular Specialisation of the Compactified Jacobian and its applications Das, Sourav Parameswaran, A. J. Sarkar, Subham Algebraic Geometry Algebraic Topology For any positive integer $k$, let $X_k$ be a projective irreducible nodal curve with $k$ nodes. We show that the Betti numbers and the mixed Hodge numbers of the compactified Jacobian $\overline{J_{k}}$ of an irreducible nodal curve $X_k$ with $k$ nodes are the same as the Betti numbers and the mixed Hodge numbers of $J_0\times R^k$, where $J_0$ is the Jacobian of the normalisation of the irreducible nodal curve and $R$ denotes the rational nodal curve with one node. We prove it by constructing a topologically locally trivial family of projective varieties containing $\overline{J_{k}}$ and $J_0\times R^k$ as fibres. |
| title | An Equisingular Specialisation of the Compactified Jacobian and its applications |
| topic | Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2107.12259 |