Gerbes of chiral differential operators. III

Abstract

This note is a sequel to "Gerbes of chiral differential operators. II", math.AG/0003170. We study gerbes of chiral differential operators acting on the exterior algebra $\Lambda E$ of a vector bundle over a smooth algebraic variety $X$. When $E={\Omega }_X^1$ this gerbe admits a canonical global section which coincides with the chiral de Rham complex of $X$.

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