On the Motivic Class of the Moduli Stack of Twisted $G$-Covers

TL;DR

This paper computes the motivic class of the stack of twisted G-covers of genus 0 curves within the Grothendieck group of stacks, expressing it via loci over smooth bases, advancing understanding of moduli stacks in algebraic geometry.

Contribution

It provides an explicit description of the motivic class of the moduli stack of twisted G-covers, linking it to smooth base loci, which is a novel computation in the field.

Findings

Explicit motivic class formula for twisted G-covers

Connection between stack classes and smooth base loci

Advancement in understanding moduli stacks of covers

Abstract

We describe the class, in the Grothendieck group of stacks, of the stack of twisted $G$-covers of genus $0$ curves, in terms of the loci corresponding to covers over smooth bases.