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Vertex algebras and the formal loop space

Mikhail KapranovEric Vasserot — 2004

Publications Mathématiques de l'IHÉS

We construct a certain algebro-geometric version ( X ) of the free loop space for a complex algebraic variety X. This is an ind-scheme containing the scheme 0 ( X ) of formal arcs in X as studied by Kontsevich and Denef-Loeser. We describe the chiral de Rham complex of Malikov, Schechtman and Vaintrob in terms of the space of formal distributions on ( X ) supported in 0 ( X ) . We also show that ( X ) possesses a factorization structure: a certain non-linear version of a vertex algebra structure. This explains the heuristic...

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