# Elliptic genus of singular algebraic varieties and quotients

## TL;DR

This paper explores different versions of the two-variable elliptic genus, focusing on equivariant cases and their applications to non-compact GITs and theoretical physics models.

## Contribution

It introduces and analyzes properties of elliptic genera in singular and quotient varieties, especially in the context of non-compact GITs and supersymmetric theories.

## Key findings

- Properties of equivariant elliptic genus established
- Elliptic genera for non-compact GITs characterized
- Applications to Witten's phases in N=2 theories

## Abstract

We discuss the basic properties of various versions of two variable elliptic genus with special attention to the equivariant elliptic genus. The main applications are to the elliptic genera attached to non-compact GITs, including the elliptic genera of Witten's phases on $N=2$ theories.