论文标题
$ \ mathsf {sl}（2，\ mathbb {c}）$ Hitchin System的$ \ Mathsf {sl}奇异纤维的半亚伯光谱数据
Semi-abelian spectral data for singular fibres of the $\mathsf{SL}(2,\mathbb{C})$-Hitchin system
论文作者
论文摘要
我们描述了$ \ mathsf {sl}（2，\ mathbb {c}）$的奇异纤维的光谱数据 - 带有不可约和减少的光谱曲线的Hitchin纤维。使用Hecke转换，我们通过Prym品种上的纤维束对这些奇异空间进行了分层。通过分析Hecke转换的参数空间，这将单数hitchin纤维描述为阿贝尔托架上阿贝尔群捆绑的压缩。我们证明，大量的奇异纤维本身就是Prym品种上的纤维束。作为应用，我们研究了奇异的hitchin纤维的不可约组件，并提供了$ \ mathsf {sl}（2，\ mathbb {r}）$ - Higgs捆绑包的描述。
We describe spectral data for singular fibres of the $\mathsf{SL}(2,\mathbb{C})$-Hitchin fibration with irreducible and reduced spectral curve. Using Hecke transformations we give a stratification of these singular spaces by fibre bundles over Prym varieties. By analysing the parameter spaces of Hecke transformations this describes the singular Hitchin fibres as compactifications of abelian group bundles over abelian torsors. We prove that a large class of singular fibres are themselves fibre bundles over Prym varieties. As applications we study irreducible components of singular Hitchin fibres and give a description of $\mathsf{SL}(2,\mathbb{R})$-Higgs bundles in terms of these semi-abelian spectral data.
