论文标题
高渗性希钦系统和基尔chhoff多项式
Hypertoric Hitchin systems and Kirchhoff polynomials
论文作者
论文摘要
我们定义了高渗Hitchin系统的形式代数类似物，其复杂的分析对应物是由Hausel-Proudfoot定义的。这些是与图形相关的代数完全可集成的系统。我们研究了由此产生的Abelian品种家族的Tamagawa数量的变化，并表明该图的Kirchhoff多项式描述了它。特别是，这使我们能够计算他们的P-ADIC量。我们通过指出这些空间承认保留热带化的卷来结束这篇文章。
We define a formal algebraic analogue of hypertoric Hitchin systems, whose complex-analytic counterparts were defined by Hausel-Proudfoot. These are algebraic completely integrable systems associated to a graph. We study the variation of the Tamagawa number of the resulting family of abelian varieties, and show that it is described by the Kirchhoff polynomial of the graph. In particular, this allows us to compute their p-adic volumes. We conclude the article by remarking that these spaces admit a volume preserving tropicalisation.
