论文标题
Kirchhoff的Prym品种定理
Kirchhoff's theorem for Prym varieties
论文作者
论文摘要
我们证明了Kirchhoff的矩阵树定理的类似物，用于计算热带Prym品种的体积，以用于度量图的双层盖。我们通过仔细研究热带亚伯-prym图的仔细研究来解释热带Prym品种的半规范分解。特别是，我们表明该地图是谐波的，确定了分解的每个单元格的程度，并证明其全局度为$ 2^{g-1} $。一路上，我们使用Ihara Zeta函数为有限图提供了类似结果的新证明。作为对手，Sebastian Casalaina-Martin的附录表明，代数Abel-Prym地图的程度也为$ 2^{G-1} $。
We prove an analogue of Kirchhoff's matrix tree theorem for computing the volume of the tropical Prym variety for double covers of metric graphs. We interpret the formula in terms of a semi-canonical decomposition of the tropical Prym variety, via a careful study of the tropical Abel-Prym map. In particular, we show that the map is harmonic, determine its degree at every cell of the decomposition, and prove that its global degree is $2^{g-1}$. Along the way, we use the Ihara zeta function to provide a new proof of the analogous result for finite graphs. As a counterpart, the appendix by Sebastian Casalaina-Martin shows that the degree of the algebraic Abel-Prym map is $2^{g-1}$ as well.
