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The chiral de Rham complex is a sheaf of vertex algebras   $\Omega ^{{\rm ch}}_M$   on any nonsingular algebraic variety or complex manifold   $M$  , which contains the ordinary de Rham complex as the weight zero subspace. We show that when   $M$   is a Kummer surface, the algebra of global sections is isomorphic to an   $N=4$   superconformal vertex algebra with central charge 6. Previously,   $\mathbb {C}\mathbb {P}^n$   was the only manifold where a complete description of the global section algebra was known.

The Global Sections of the Chiral de Rham Complex on a Kummer Surface