The global sections of the chiral de Rham complex on a Kummer surface

TL;DR

This paper demonstrates that for a Kummer surface, the algebra of global sections of the chiral de Rham complex is isomorphic to the N=4 superconformal vertex algebra with central charge 6, extending known results beyond CP^n.

Contribution

It provides the first explicit description of the global sections of the chiral de Rham complex on a Kummer surface, revealing a deep algebraic structure.

Findings

Global sections form an N=4 superconformal vertex algebra

Kummer surface case extends previous known examples

Algebra is isomorphic to a well-known superconformal algebra

Abstract

The chiral de Rham complex is a sheaf of vertex algebras {\Omega}^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 the N = 4 superconformal vertex algebra with central charge 6. Previously, CP^n was the only manifold where a complete description of the global section algebra was known.