热带谱曲线与可积元胞自动机
Tropical spectral curves and integrable cellular automata
摘要：
提出了一种利用热带谱曲线及其雅可比矩阵研究周期边界条件下可积元胞自动机的方法。本文在热带超椭圆曲线上引入了从等层集到因子类的热带形式的特征向量映射。我们还提供了一些有关的因子类和雅可比矩阵。最后，我们将我们的方法应用到周期盒球系统中，并阐明了为解决其初值问题而引入的实环面的代数几何意义。
英文摘要：
We propose a method to study the integrable cellular automata with periodic boundary conditions, via the tropical spectral curve and its Jacobian. We introduce the tropical version of eigenvector map from the isolevel set to a divisor class on the tropical hyperelliptic curve. We also provide some conjectures related to the divisor class and the Jacobian. Finally, we apply our method to the periodic box and ball system and clarify the algebro-geometrical meaning of the real torus introduced for its initial value problem.
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