2004/12/21 by Anatoly Libgober, Libgober, Anatoly, Matthew Szczesny +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.AG #math.QA
paper · pdf · doi:10.48550/arxiv.math/0412422
arxiv created 2004/12/21 · openalex publication_date 2004/12/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a compact complex algebraic variety with an effective action of a finite group G, and a class α∈ H2(G,U(1)), we introduce an orbifold elliptic genus with discrete torsion α, denoted Ellαorb(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, Ellαorb(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.