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McKay correspondence for elliptic genera. (English) Zbl 1153.58301

Summary: We establish a correspondence between orbifold and singular elliptic genera of a global quotient. While the former is defined in terms of the fixed point set of the action, the latter is defined in terms of the resolution of singularities. As a byproduct, the second quantization formula of Dijkgraaf, Moore, Verlinde and Verlinde is extended to arbitrary Kawamata log-terminal pairs.

MSC:

58J26 Elliptic genera
11F23 Relations with algebraic geometry and topology
11F50 Jacobi forms
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
55N34 Elliptic cohomology
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