The Hitchin moduli stack $\mathcal M_G$ is essentially the total space of the cotangent bundle of $\mathrm{Bun}_G$, therefore perverse sheaves on $\mathrm{Bun}_G$ are related to the symplectic geometry of $\mathcal M_G$ via the characteristic cycle construction. — 恽之伟, Hitchin-type moduli spaces in automorphic representation theory
主丛的模空间在主丛 $E$ 处的切空间, 即 $E$ 的无穷小形变的空间 $H^1(X,\operatorname{ad}E)$, 由 Serre 对偶等同于 $H^0(X,\mathcal K_X\otimes\operatorname{ad}E)$, 其元素称为 Higgs 场.