Singular elliptic genus of normal surfaces

TL;DR

This paper introduces a new singular elliptic genus for normal surfaces, proving its invariance under birational transformations and demonstrating its generalization of existing genera like the Borisov-Libgober and Batyrev-Veys versions.

Contribution

It defines a novel singular elliptic genus for normal surfaces and establishes its invariance and generalization properties.

Findings

Singular elliptic genus is a birational invariant.

Generalizes previous notions of elliptic and stringy genera.

Unifies different genus concepts for normal surfaces.

Abstract

We define the singular elliptic genus for arbitrary normal surfaces, prove that it is a birational invariant, and show that it generalizes the singular elliptic genus of Borisov and Libgober and the stringy $\chi_y$ genus of Batyrev and Veys.