Elliptic Genera of singular varieties, orbifold elliptic genus and chiral deRham complex

TL;DR

This paper surveys recent advances in the elliptic genus of singular varieties, including orbifold elliptic genus and chiral de Rham complex, and computes generating functions for symmetric products, extending classical results.

Contribution

It introduces new methods for computing elliptic genera of singular varieties and generalizes classical results to symmetric products.

Findings

Derived a generating function for elliptic genera of symmetric products.

Extended classical results of Macdonald and Zagier to singular varieties.

Provided a survey of recent developments in orbifold elliptic genus.

Abstract

This paper surveys the authors recent work on two variable elliptic genus of singular varieties. The last section calculates a generating function for the elliptic genera of symmetric products. This generalizes the classical results of Macdonald and Zagier.