Tropical Poincaré bundle, Fourier-Mukai transform, and a generalized Poincaré formula
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917958956089344 |
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| author | Ghosh, Soham Shokrieh, Farbod |
| author_facet | Ghosh, Soham Shokrieh, Farbod |
| contents | We construct a tropical analogue of the Poincaré bundle and prove a (cohomological) Fourier-Mukai transform for real tori with integral structures. We then prove a tropical analogue of Beauville's generalized Poincaré formula for polarized abelian varieties. Some consequences include a geometric Riemann-Roch theorem for tropical abelian varieties, as well as a tropical Poincaré-Prym formula which was recently conjectured by Röhrle and Zakharov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12835 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tropical Poincaré bundle, Fourier-Mukai transform, and a generalized Poincaré formula Ghosh, Soham Shokrieh, Farbod Algebraic Geometry Combinatorics 14T20, 11G10, 14C25, 14C17, 14H40, 14C40 We construct a tropical analogue of the Poincaré bundle and prove a (cohomological) Fourier-Mukai transform for real tori with integral structures. We then prove a tropical analogue of Beauville's generalized Poincaré formula for polarized abelian varieties. Some consequences include a geometric Riemann-Roch theorem for tropical abelian varieties, as well as a tropical Poincaré-Prym formula which was recently conjectured by Röhrle and Zakharov. |
| title | Tropical Poincaré bundle, Fourier-Mukai transform, and a generalized Poincaré formula |
| topic | Algebraic Geometry Combinatorics 14T20, 11G10, 14C25, 14C17, 14H40, 14C40 |
| url | https://arxiv.org/abs/2503.12835 |