Chiral Hodge Cohomology and Mathieu Moonshine

Author:

Song Bailin1

Affiliation:

1. Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China

Abstract

Abstract We construct a filtration of chiral Hodge cohomolgy of a K3 surface $X$, such that its associated graded object is a unitary representation of the $\mathcal{N}=4$ superconformal vertex algebra with central charge $c=6$ and its subspace of primitive vectors has the property; its equivariant character for a symplectic automorphism $g$ of finite order acting on $X$ agrees with the McKay–Thompson series for $g$ in Mathieu moonshine.

Funder

National Natural Science Foundation of China

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

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4. K3 Surfaces, $N=4$ Dyons and the Mathieu Group ${M}_{24}$;Cheng;Commun. Number Theory Phys.,2010

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