Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 107, 31 pages      arXiv:2212.14722      https://doi.org/10.3842/SIGMA.2023.107
Contribution to the Special Issue on Enumerative and Gauge-Theoretic Invariants in honor of Lothar Göttsche on the occasion of his 60th birthday

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

Massimo Bagnarol a and Fabio Perroni b
a) Dipartimento di Ingegneria e Architettura, Università degli Studi di Trieste, via Valerio 6/1, 34127 Trieste, Italy
b) Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, via Valerio 12/1, 34127 Trieste, Italy

Received January 02, 2023, in final form December 19, 2023; Published online December 27, 2023

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.

Key words: moduli spaces of covers; Grothendieck group of stacks.

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