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Vertex algebras and the formal loop space

M. Kapranov·E. Vasserot
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Abstract

We introduce an algebro-geometric version of the free loop space for any scheme X of finite type. This is an ind-scheme of ind-infinite type containing the scheme of formal germs of curves on X. Then, we give a direct geometric construction, for smooth X, of the chiral de Rham complex of X (introduced by Malikov, Schechtman and Vaintrob).

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M. Kapranov, E. Vasserot. 2004-07-09. Vertex algebras and the formal loop space. https://arxiv.org/abs/math/0107143

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