论文标题
CERESA类和热带曲线
The Ceresa class and tropical curves of hyperelliptic type
论文作者
论文摘要
我们定义了一个名为Ceresa-Zharkov类的图形$ G $的新代数不变，并且仅当$ g $是过度ellelliptic类型的情况下，这是微不足道的，同等地，$ g $在4个角度或3个循环的循环上没有完整的图形。选择边缘长度后，此类专门针对热带曲线的代数不变，其基础图$ g $与CERESA循环密切相关，该代数与代数曲线定义了$ \ Mathbb {C}（c}（\！（t）\！）\！）$。
We define a new algebraic invariant of a graph $G$ called the Ceresa-Zharkov class and show that it is trivial if and only if $G$ is of hyperelliptic type, equivalently, $G$ does not have as a minor the complete graph on 4 vertices or the loop of 3 loops. After choosing edge-lengths, this class specializes to an algebraic invariant of a tropical curve with underlying graph $G$ that is closely related to the Ceresa cycle for an algebraic curve defined over $\mathbb{C}(\!(t)\!)$.
