论文标题
Prym-Narasimhan-Ramanan主要捆绑点的构造
A Prym-Narasimhan-Ramanan construction of principal bundle fixed points
论文作者
论文摘要
让$ x $成为紧凑的Riemann Surface，而$ G $是一个连接的还原复合物lie Group，中央$ z $。考虑$ x $上的polystable主塑形$ g $捆的模量$ m（x，g）$。 $ m（x，z，z）$ h^1（x，z）$ h^1（x，z）$ $ z $ - 捆绑$ z $捆绑在$ m（x，g）上的$ x $（x，g）$，由乘法$ z \ times g \ tog。$ g。让$γ$是$ h^1（x，z）$的有限亚组。我们的目标是在$γ$的动作下找到一个Prym-Narasimhan-Ramanan型结构，以描述$ m（x，g）$的固定点。这种结构中的主要成分是在Arxiv中开发的$ x $ of twisted eproivariant捆绑包的理论：2208.0902（2）。
Let $X$ be a compact Riemann surface and $G$ be a connected reductive complex Lie group with centre $Z$. Consider the moduli space $M(X,G)$ of polystable principal holomorphic $G$-bundles on $X$. There is an action of the group $H^1(X,Z)$ of isomorphism classes of $Z$-bundles over $X$ on $M(X,G)$ induced by the multiplication $Z\times G\to G.$ Let $Γ$ be a finite subgroup of $H^1(X,Z)$. Our goal is to find a Prym--Narasimhan--Ramanan-type construction to describe the fixed points of $M(X,G)$ under the action of $Γ$. A main ingredient in this construction is the theory of twisted equivariant bundles on an étale cover of $X$ developed in arXiv:2208.0902(2).
