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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.12812 |
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| _version_ | 1866911045928353792 |
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| author | Barajas, G. García-Prada, O. |
| author_facet | Barajas, G. García-Prada, O. |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_12812 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Prym-Narasimhan-Ramanan construction of principal bundle fixed points Barajas, G. García-Prada, O. Algebraic Geometry 14H60 (Primary) 53C07, 58D19 (Secondary) 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). |
| title | A Prym-Narasimhan-Ramanan construction of principal bundle fixed points |
| topic | Algebraic Geometry 14H60 (Primary) 53C07, 58D19 (Secondary) |
| url | https://arxiv.org/abs/2211.12812 |