(Log) Chiral de Rham complex and $A_n$-singular surfaces

TL;DR

This paper constructs the chiral de Rham complex on algebraic surfaces with rational $A_n$-type singularities and provides an explicit character formula for the chiral structure sheaf.

Contribution

It introduces a new construction of the chiral de Rham complex specifically for surfaces with $A_n$-type singularities and derives an explicit character formula.

Findings

Construction of the chiral de Rham complex on $A_n$-singular surfaces

Explicit character formula for the chiral structure sheaf

Extension of chiral de Rham theory to singular algebraic surfaces

Abstract

We present a construction of the chiral de Rham complex over an algebraic surface with at most rational singularities of $A_n$-type. An explicit formula for the character of the chiral structure sheaf is also provided.