论文标题
在覆盖范围内的Hitchin纤维
Hitchin fibration under ramified coverings
论文作者
论文摘要
我们有兴趣研究抛物线希格斯束的模量空间中Hitchin纤维的变化，这是在覆盖范围的作用下的。考虑到紧凑的Riemann表面之间的两个地图$π$：y $ \ rightarrow $ x，我们可能会将希格斯捆绑包从x到y，抬起的希格斯捆绑包往往具有许多明显的奇异性，那么我们进行了合适的民间转换以消除它们。该对应关系保留了Hitchin纤维，然后其限制对一般纤维的限制给出了Abelian品种之间的地图。本文的目的是描述这张地图。
We are interested in studying the variation of the Hitchin fibration in moduli spaces of parabolic Higgs bundles, under the action of a ramified covering. Given a degree two map $π$ : Y $\rightarrow$ X between compact Riemann surfaces, we may pull back a Higgs bundle from X to Y , the lifted Higgs bundle tends to have many apparent singularities, then we perform a suitable birational transformation in order to eliminate them. This correspondence preserves the Hitchin fibrations and then its restriction to a general fiber gives a map between Abelian varieties. The aim of this paper is to describe this map.
