论文标题
对希格斯捆绑模量空间和扭曲的模层结构的有限小组动作
Finite group actions on Higgs bundle moduli spaces and twisted equivariant structures
论文作者
论文摘要
我们考虑$ g $ -higgs的模量$ {\ cal m}（g）$ $ g $ -higgs捆绑包，而紧凑型Riemann Surface $ x $，其中$ g $是一个半杂色的综合体系，并研究了有限群$γ$ $ {\ cal m}（g cal m}（g）$ $ $ $ $ g的$＆k的动作$γ$。此操作的定点子变量由$ g $ -higgs捆绑的模量捆绑，配备了一定扭曲的$γ$ equivariant结构，涉及$ 2 $ cocycle $ 2 $ cocycle为$ g $中心的$ 2 $ cocycycle。该工会是由$ g $的隔行组中的非亚伯式第一首共同组合$γ$对众所周知的。我们还通过非 - 阿伯里亚杂货店的扭曲的epivariant版本来描述$ g $中$ x $ in $ g $的基本组的固定点，该版本涉及$ x $的$γ$ equivariant基本组。
We consider the moduli space ${\cal M}(G)$ of $G$-Higgs bundles over a compact Riemann surface $X$, where $G$ is a semisimple complex Lie group, and study the action of a finite group $Γ$ on ${\cal M}(G)$ induced by a holomorphic action of $Γ$ on $X$ and $G$, and a character of $Γ$. The fixed-point subvariety for this action is given by a union of moduli spaces of $G$-Higgs bundles equipped with a certain twisted $Γ$-equivariant structure involving a $2$-cocycle of $Γ$ with values in the centre of $G$. This union is paremeterized by the non-abelian first cohomology set of $Γ$ in the adjoint group of $G$. We also describe the fixed points in the moduli space of representations of the fundamental group of $X$ in $G$, via a twisted equivariant version of the non-abelian Hodge correspondence, which involves the $Γ$-equivariant fundamental group of $X$.
