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Mathematics > Algebraic Geometry

arXiv:1809.07501 (math)
[Submitted on 20 Sep 2018]

Title:K3 surfaces with a pair of commuting non-symplectic involutions

Authors:Frank Reidegeld
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Abstract:We study K3 surfaces with a pair of commuting involutions that are non-symplectic with respect to two anti-commuting complex structures that are determined by a hyper-Kähler metric. One motivation for this paper is the role of such $\mathbb{Z}^2_2$-actions for the construction of $G_2$-manifolds. We find a large class of smooth K3 surfaces with such pairs of involutions, but we also pay special attention to the case that the K3 surface has ADE-singularities. Therefore, we introduce a special class of non-symplectic involutions that are suitable for explicit calculations and find 320 examples of pairs of involutions that act on K3 surfaces with a great variety of singularities.
Comments: 30 pages
Subjects: Algebraic Geometry (math.AG); Differential Geometry (math.DG)
MSC classes: 14J28, 53C26
Cite as: arXiv:1809.07501 [math.AG]
  (or arXiv:1809.07501v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1809.07501

Submission history

From: Frank Reidegeld [view email]
[v1] Thu, 20 Sep 2018 07:15:51 UTC (24 KB)
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