arxiv: 1309.2671 · v2 · pith:QTZBRYGMnew · submitted 2013-09-10 · 🧮 math.QA · hep-th· math.NT

Mathieu Moonshine and the Geometry of K3 Surfaces

Thomas Creutzig , Gerald Hoehn This is my paper

classification 🧮 math.QA hep-thmath.NT

keywords groupmathieucomplexellipticgenusmoonshinesurfacesurfaces

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We compare the moonshine observation of Eguchi, Ooguri and Tachikawa relating the Mathieu group M_24 and the complex elliptic genus of a K3 surface with the symmetries of geometric structures on K3 surfaces. Two main results are that the complex elliptic genus of a K3 surface is a virtual module for the Mathieu group M_24 and also for a certain vertex operator superalgebra V^G where G is the holonomy group.

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Mathieu Moonshine and the Geometry of K3 Surfaces

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