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arXiv · 2211.12812

A Prym-Narasimhan-Ramanan construction of principal bundle fixed points

G. Barajas·O. García-Prada
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Abstract

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 $\Gamma$ 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 $\Gamma$. A main ingredient in this construction is the theory of twisted equivariant bundles on an \'etale cover of $X$ developed in arXiv:2208.0902(2).

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G. Barajas, O. García-Prada. 2022-11-23. A Prym-Narasimhan-Ramanan construction of principal bundle fixed points. https://arxiv.org/abs/2211.12812

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