当Jacobian为Comessatti时，Hutchinson-Weber对合完全退化
Hutchinson-Weber involutions degenerate exactly when the Jacobian is Comessatti
摘要：
研究亏格为两条曲线$C$的Jacobian Kummer曲面$X$.证明了$X$上的Hutchinson-Weber对合退化当且仅当Jacobian $J(C)$是Comessatti.给出了几个等价的条件，其中包括经典的Humbert定理.关键的概念是韦伯六面体。我们包括了对它们的解释，并讨论了各种韦伯六角体的主要定理的条件之间的依赖关系。其结果是“等价于对偶六”。我们也给出了相关的模空间的详细描述。作为应用，给出了一般Hutchinson-Weber对合的修补子群计算的概念性证明。
英文摘要：
We consider the Jacobian Kummer surface $X$ of a genus two curve $C$. We prove that the Hutchinson-Weber involution on $X$ degenerates if and only if the Jacobian $J(C)$ is Comessatti. Also we give several conditions equivalent to this, which include the classical theorem of Humbert. The key notion is the Weber hexad. We include explanation of them and discuss the dependence between the conditions of main theorem for various Weber hexads. It results in "the equivalence as dual six". We also give a detailed description of relevant moduli spaces. As an application, we give a conceptual proof of the computation of the patching subgroup for generic Hutchinson-Weber involutions.
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