Riemann-Roch coefficients for Kleinian orbisurfaces
arXiv:2103.10767 · doi:10.1007/s40574-023-00353-z
Abstract
Suppose is a smooth, proper, and tame Deligne-Mumford stack. Toën's Grothendieck-Riemann-Roch theorem requires correction terms, involving components of the inertia stack, to the standard formula for schemes. We give a brief overview of Toën's Grothendieck-Riemann-Roch theorem, and explicitly compute the correction terms in the case of an orbifold surface with stabilizers of types ADE.
V1: 10 pages. This work originates from the appendix of arxiv:2001.09139 (not included in forthcoming new version), now expanded and turned into independent submission. All comments welcome! V2: 13 pages, added an exposition of the Riemann-Roch theorem for Deligne-Mumford stacks aimed at non-experts. To appear in Bollettino dell'Unione Matematica Italiana