Generating series of classes of Hilbert schemes of points on orbifolds

TL;DR

This paper explores the use of power structures over the Grothendieck ring to analyze generating series of Hilbert schemes of points on complex orbifolds, providing a new algebraic approach.

Contribution

It introduces a novel application of power structures to study generating series of Hilbert schemes on orbifolds, advancing algebraic geometric methods.

Findings

Derived new formulas for generating series of Hilbert schemes on orbifolds

Connected power structures with Hilbert scheme classes

Provided algebraic tools for future research in orbifold geometry

Abstract

In this short note we use the notion of power structure over the Grothendieck ring of complex algebraic varieties to study generating series of classes of Hilbert schemes of points on complex orbifolds.