Discrete torsion, orbifold elliptic genera, and the chiral de Rham complex

Details Discrete torsion, orbifold elliptic genera, and the chiral de Rham complex Discrete torsion, orbifold elliptic genera, and the chiral de Rham complex

2004-12-21

arxiv.org/abs/math/0412422v1

Mathematics

Algebraic Geometry

Scientific paper

Given a compact complex algebraic variety with an effective action of a finite group $G$, and a class $\alpha \in H^2(G,U(1))$, we introduce an orbifold elliptic genus with discrete torsion $\alpha$, denoted $Ell^{\alpha}_{orb}(X,G, q, y)$. We give an interpretation of this genus in terms of the chiral de Rham complex attached to the orbifold $[X/G]$. If $X$ is Calabi-Yau and $G$ preserves the volume form, $Ell^{\alpha}_{orb}(X,G, q, y)$ is a weak Jacobi form. We also obtain a formula for the generating function of the elliptic genera of symmetric products with discrete torsion.

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