The tropical $n$-gonal construction
| Autor: | Röhrle, Felix, Zakharov, Dmitry |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We give a purely tropical analogue of Donagi's $n$-gonal construction and investigate its combinatorial properties. The input of the construction is a harmonic double cover of an $n$-gonal tropical curve. For $n = 2$ and a dilated double cover, the output is a tower of the same type, and we show that the Prym varieties of the two double covers are dual tropical abelian varieties. For $n=3$ and a free double cover, the output is a tetragonal tropical curve with dilation profile nowhere $(2,2)$ or $(4)$, and we show that the construction can be reversed. Furthermore, the Prym variety of the double cover and the Jacobian of the tetragonal curve are isomorphic as principally polarized tropical abelian varieties. Our main tool is tropical homology theory, and our proofs closely follow the algebraic versions. Comment: Shortened and streamlined Section 2 (the $n$-gonal construction). Major revisions in Section 4 (replaced construction of Prym^pp with Prym_c and corrected the universal property of the Prym variety). Fixed proof of Theorem 1.1 in Section 5 |
| Databáze: | arXiv |
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