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| Format: | Preprint |
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2025
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| Accès en ligne: | https://arxiv.org/abs/2502.05624 |
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| _version_ | 1866916605662855168 |
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| author | Cobigo, Lou-Jean Leila |
| author_facet | Cobigo, Lou-Jean Leila |
| contents | This paper is the second in a series of two papers which study the phenomenon of tropical split Jacobians. The first paper is a contemplative study, embedded in the broader context of exploring connections between the category of tropical abelian varieties (tav), $\mathbb{T}\mathcal{A}$, and the category of tropical curves, $\mathbb{T}\mathcal{C}$. Tropical split Jacobians take on different forms depending on whether we look at them in $\mathbb{T}\mathcal{A}$ or $\mathbb{T}\mathcal{C}$: They appear either as 2 dimensional tavs that decompose into a product of two elliptic curves, or as a pair of optimal coverings. [11] examines both and then focuses on how optimal covers give rise to split Jacobians. This paper takes a different approach. Instead of looking at the phenomenon as a whole, we analyze its building blocks, a pair of elliptic curves together with a finite subgroup of their product, and how to reassemble them into a Jacobian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05624 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tropical split Jacobians of curves of genus 2 II Cobigo, Lou-Jean Leila Algebraic Geometry Combinatorics This paper is the second in a series of two papers which study the phenomenon of tropical split Jacobians. The first paper is a contemplative study, embedded in the broader context of exploring connections between the category of tropical abelian varieties (tav), $\mathbb{T}\mathcal{A}$, and the category of tropical curves, $\mathbb{T}\mathcal{C}$. Tropical split Jacobians take on different forms depending on whether we look at them in $\mathbb{T}\mathcal{A}$ or $\mathbb{T}\mathcal{C}$: They appear either as 2 dimensional tavs that decompose into a product of two elliptic curves, or as a pair of optimal coverings. [11] examines both and then focuses on how optimal covers give rise to split Jacobians. This paper takes a different approach. Instead of looking at the phenomenon as a whole, we analyze its building blocks, a pair of elliptic curves together with a finite subgroup of their product, and how to reassemble them into a Jacobian. |
| title | Tropical split Jacobians of curves of genus 2 II |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2502.05624 |