The universal sheaf as an operator

TL;DR

This paper generalizes the computation of the universal sheaf on moduli spaces of sheaves on surfaces, representing it as an operator from symmetric polynomials to K-theory, extending previous work to broader contexts.

Contribution

It introduces a new operator framework for the universal sheaf applicable to arbitrary rank and smooth surfaces, broadening the scope of prior models.

Findings

Universal sheaf expressed as an operator from symmetric polynomials to K(M)

Generalization of Carlsson-Nekrasov-Okounkov's approach

Applicable to arbitrary rank and smooth surfaces

Abstract

We compute the universal sheaf of moduli spaces M of sheaves on a surface S, as an operator {Symmetric Polynomials} $\rightarrow$ K(M), thus generalizing the viewpoint of Carlsson-Nekrasov-Okounkov to arbitrary rank and general smooth surfaces.