论文标题
$ \ MATHFRAK {SL}（2）$ - 类型符号和奇数正交Hitchin系统的单数纤维
$\mathfrak{sl}(2)$-type singular fibres of the symplectic and odd orthogonal Hitchin system
论文作者
论文摘要
我们定义和参数所谓的$ \ mathfrak {sl}（2）$ - 类型的型纤维纤维{sp}（sp}（2n，\ mathbb {c}）$ - 和$ \ mathsf {so}（so}（2N+1，\ athbb {c} c}）这些是（单数）的hitchin纤维，其中光谱曲线诱导了第二个Riemann Surface $ y $的两片覆盖物。这可以标识$ \ mathfrak {sl}（2）$ - 键入Hitchin纤维，带有$ \ Mathsf {Slsf {sl}（2，\ Mathbb {C}）$ - 分别为$ \ Mathsf {psl {psl}（2，2，\ MathBB {C}）$ - $ y $ $ y $。我们通过半亚伯频谱数据对这些奇异空间进行了分层，研究其不可还原成分，并获得对第一个退化的全球描述。比较$ \ mathfrak {sl}（2）$ - 为两个Langlands双重组的Hitchin Fibers的半亚伯频谱数据，我们将常规Hitchin纤维的众所周知的Langlands双重性扩展到$ \ MATHFRAK {SL}（SL}（2）$ - 类型Hitchin Hitchin Fibers。最后，我们为$ \ mathfrak {sl}（2）$ - 类型的Higgs捆绑包的脱钩Hitchin方程构建解决方案。我们猜想这些是沿射线限制指标到模量空间的末端。
We define and parametrise so-called $\mathfrak{sl}(2)$-type fibres of the $\mathsf{Sp}(2n,\mathbb{C})$- and $\mathsf{SO}(2n+1,\mathbb{C})$-Hitchin system. These are (singular) Hitchin fibres, where the spectral curve induces a two-sheeted covering of a second Riemann surface $Y$. This identifies the $\mathfrak{sl}(2)$-type Hitchin fibres with fibres of an $\mathsf{SL}(2,\mathbb{C})$- respectively $\mathsf{PSL}(2,\mathbb{C})$-Hitchin map on $Y$. We give a stratification of these singular spaces by semi-abelian spectral data, study their irreducible components and obtain a global description of the first degenerations. Comparing the semi-abelian spectral data of $\mathfrak{sl}(2)$-type Hitchin fibres for the two Langlands dual groups, we extend the well-known Langlands duality of regular Hitchin fibres to $\mathfrak{sl}(2)$-type Hitchin fibres. Finally, we construct solutions to the decoupled Hitchin equation for Higgs bundles of $\mathfrak{sl}(2)$-type. We conjecture these to be limiting metrics along rays to the ends of the moduli space.
