Elliptic classes, McKay correspondence and theta identities

2019/09/16 by Mikosz, Malgorzata, Weber, Andrzej
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1909.07303

Abstract

We revisit the construction of elliptic class given by Borisov and Libgober for singular algebraic varieties. Assuming torus action we adjust the theory to equivariant local situation. We study theta function identities having geometric origin. In the case of quotient singularities \mathbb Cⁿ/G, where G is a finite group the theta identities arise from McKay correspondence. The symplectic singularities are of special interest. The Du Val surface singularity A_n leads to a remarkable formula.

Related

• Elliptic classes, McKay correspondence and theta identities
• Geometric and arithmetic theta correspondences
• Equivariant Elliptic Genera and Local McKay Correspondences
• Theta functions and mirror symmetry
• Equivariant Hirzebruch classes and Molien series of quotient singularities