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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Enriques Surfaces of Hutchinson–Göpel Type and Mathieu Automorphisms
verfasst von : Shigeru Mukai, Hisanori Ohashi
Erschienen in: Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds
Verlag: Springer New York
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Abstract
We study a class of Enriques surfaces called of Hutchinson–Göpel type. Starting with the projective geometry of Jacobian Kummer surfaces, we present the Enriques’ sextic expression of these surfaces and their intrinsic symmetry by \(G = C_{2}^{3}\). We show that this G is of Mathieu type and conversely, that these surfaces are characterized among Enriques surfaces by the group action by \(C_{2}^{3}\) with prescribed topological type of fixed point loci. As an application, we construct Mathieu type actions by the groups \(C_{2} \times \mathfrak{A}_{4}\) and \(C_{2} \times C_{4}\). Two introductory sections are also included.