论文标题
群集图片，用于等级的Hitchin纤维两个Higgs捆绑包
Cluster pictures for Hitchin fibers of rank two Higgs bundles
论文作者
论文摘要
令$φ\ colon x \ rightarrow y $为奇数特征的本地字段$ f $上的平滑曲线的两个学位。假设$ y $使用良好的减少，我们使用覆盖$φ$的分支基因座的数据描述了曲线$ x $的半稳定性标准。如果$ x $具有半稳定的减少，我们描述了$ f以上的$ x $的最小常规型号的双图。$我们通过采用针对$ y $不一定是合理曲线的过度椭圆形曲线定义的群集图片的概念来做到这一点。使用这些结果，我们描述了Hitchin纤维的P-ADIC体积在等级2扭曲的Higgs束的模量空间的半稳定基因座上的变化。
Let $φ\colon X\rightarrow Y$ be a degree two Galois cover of smooth curves over a local field $F$ of odd characteristic. Assuming that $Y$ has good reduction, we describe a semi-stability criterion for the curve $X$, using the data of the branch locus of the covering $φ$. In the case that $X$ has semi-stable reduction, we describe the dual graph of the minimal regular model of $X$ over $F.$ We do this by adopting the notion of cluster picture defined for hyperelliptic curves for the case where $Y$ is not necessarily a rational curve. Using these results, we describe the variation of the p-adic volume of Hitchin fibers over the semi-stable locus of the moduli space of rank 2 twisted Higgs bundles.
