论文标题
通过可半曲线的光谱数据压缩两个Hitchin系统
Compactifying the rank two Hitchin system via spectral data on semistable curves
论文作者
论文摘要
我们将有理图的分辨率研究到稳定曲线的模量空间，该曲线与Hitchin底座相关的光谱曲线。在等级第二案例中，答案是根据[BCGGM3]中引入的二次多尺度差异空间给出的。该空间定义了$ \ mathrm {gl}（2，\ mathbb {c}）$ - Hitchin base的常规基因座的压实（项目化），并通过压实的尖头稳定曲线的jacobians提供了Hitchin系统的压实。我们展示了如何使用经典的$ \ mathrm {gl}（2，\ mathbb {c}）$ - 和$ \ mathrm {sl}（2，2，\ mathbb {c}）$ - 光谱对应关系扩展到紧缩的Hitchin hitchin hitchin system，沿着可靠的封面覆盖范围$ 1 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2。
We study resolutions of the rational map to the moduli space of stable curves that associates with a point in the Hitchin base the spectral curve. In the rank two case the answer is given in terms of the space of quadratic multi-scale differentials introduced in [BCGGM3]. This space defines a compactification (of the projectivization) of the regular locus of the $\mathrm{GL}(2,\mathbb{C})$-Hitchin base and provides a compactification of the Hitchin system by compactified Jacobians of pointed stable curves. We show how the classical $\mathrm{GL}(2,\mathbb{C})$- and $\mathrm{SL}(2,\mathbb{C})$-spectral correspondence extend to the compactified Hitchin system by a correspondence along an admissible cover between torsion-free rank $1$ sheaves and (multi-scale) Higgs pairs of rank $2$.
