Galois \(E_6\)-bundles over a hyperelliptic algebraic curve. (English) Zbl 1534.14027
The author considers a hyperelliptic algebraic curve \(X\) and the moduli space \(M(E_{6})\), where \(E_{6}\) is a polystable principal bundle over \(X\). The author constructs an automorphism of \(M(E_{6})\) and the main purpose of this paper is to obtain a certain family of fixed points of this automorphism, which are described in terms of Galois \(E_{6}\)-bundles. The author first defines the notion of Galois \(G\)-bundles and then studies specifically Galois \(E_{6}\)-bundles. For background, please see [Á. A. Sancho, Rev. Unión Mat. Argent. 59, No. 1, 33–56 (2018; Zbl 1398.14039)] and [Á. Antón Sancho, Math. Scand. 122, No. 1, 53–83 (2018; Zbl 1406.14026)].
Reviewer: Aigli Papantonopoulou (Ewing)
MSC:
| 14H10 | Families, moduli of curves (algebraic) |
| 14H60 | Vector bundles on curves and their moduli |
| 57R57 | Applications of global analysis to structures on manifolds |
| 53C10 | \(G\)-structures |
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