Coble duality for Jacobian Kummer fourfolds
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918035047055360 |
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| author | Agostini, Daniele Beri, Pietro Giovenzana, Franco Ortiz, Ángel David Ríos |
| author_facet | Agostini, Daniele Beri, Pietro Giovenzana, Franco Ortiz, Ángel David Ríos |
| contents | We study projective models of generalized Kummer fourfolds via O'Grady's theta groups and the classical Coble cubic. More precisely, we establish a duality between two singular models of the generalized Kummer fourfold of a Jacobian abelian surface. We also give projective models for singular Jacobian Kummer varieties of arbitrary dimension. Along the way, we also construct a first non-natural involution on the Hilbert square of a Jacobian surface. In the appendix, we study singularities of secants of arbitrary varieties at identifiable points, following Choi, Lacini, Park and Sheridan. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14490 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coble duality for Jacobian Kummer fourfolds Agostini, Daniele Beri, Pietro Giovenzana, Franco Ortiz, Ángel David Ríos Algebraic Geometry We study projective models of generalized Kummer fourfolds via O'Grady's theta groups and the classical Coble cubic. More precisely, we establish a duality between two singular models of the generalized Kummer fourfold of a Jacobian abelian surface. We also give projective models for singular Jacobian Kummer varieties of arbitrary dimension. Along the way, we also construct a first non-natural involution on the Hilbert square of a Jacobian surface. In the appendix, we study singularities of secants of arbitrary varieties at identifiable points, following Choi, Lacini, Park and Sheridan. |
| title | Coble duality for Jacobian Kummer fourfolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2505.14490 |