Exts and Vertex Operators

TL;DR

This paper explores the K-theory classes arising from Ext groups between ideal sheaves on Hilbert schemes of a surface, expressing their Chern classes via Nakajima operators.

Contribution

It provides a new formula relating Ext-based K-theory classes to Nakajima operators, deepening understanding of Hilbert scheme geometry.

Findings

Expressed Chern classes of Ext-based virtual bundles in terms of Nakajima operators

Connected Ext groups with geometric operators on Hilbert schemes

Enhanced the algebraic understanding of Hilbert scheme K-theory

Abstract

The direct product of two Hilbert schemes of the same surface has natural K-theory classes given by the alternating Ext groups between the two ideal sheaves in question, twisted by a line bundle. We express the Chern classes of these virtual bundles in terms of Nakajima operators.