A matroidal perspective on the tropical Prym variety
| Autor: | Röhrle, Felix, Zakharov, Dmitry |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We associate a matroid $M(\widetilde{\Gamma}/\Gamma)$ to a harmonic double cover $\pi:\widetilde{\Gamma}\to \Gamma$ of metric graphs. The matroid $M(\widetilde{\Gamma}/\Gamma)$ is a geometric interpretation of Zaslavsky's signed graphic matroid. We show that the principalization $\mathrm{Prym}_p(\widetilde{\Gamma}/\Gamma)$ of the tropical Prym variety of the double cover can be reconstructed from $M(\widetilde{\Gamma}/\Gamma)$, equipped with certain additional decorations. We describe the simplification of the matroid $M(\widetilde{\Gamma}/\Gamma)$ and show that the Prym variety does not change under simplification. Comment: 31 pages |
| Databáze: | arXiv |
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