Communications in Number Theory and Physics

Volume 8 (2014)

Number 2

Mathieu moonshine and the geometry of K3 surfaces

Pages: 295 – 328

DOI: http://dx.doi.org/10.4310/CNTP.2014.v8.n2.a3

Authors

Thomas Creutzig (Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada)

Gerald Höhn (Kansas State University, Manhattan, Ks., U.S.A.)

Abstract

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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