论文标题
热带$ n $ - 基准结构
The tropical $n$-gonal construction
论文作者
论文摘要
我们提供了多纳吉$ n $ gonal结构的纯粹热带类似物，并研究了其组合特性。该结构的输入是$ n $ gonal热带曲线的谐波双盖。对于$ n = 2 $和扩张的双层盖，输出是相同类型的塔，我们表明这两个双层盖的Prym品种是双热带阿贝尔品种。对于$ n = 3 $和免费的双重盖，输出是一条四方热带曲线，没有扩张型，$（2,2）$或$（4）$，我们表明构造可以逆转。此外，双覆盖物和四方曲线的雅各布的pry量是同构的，主要是极化的热带阿伯利亚品种。我们的主要工具是热带同源性理论，我们的证明遵循代数版本。
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.
