Riemann-Roch coefficients for Kleinian orbisurfaces
Abstract
Suppose is a smooth, proper, and tame Deligne-Mumford stack. To\"en'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 To\"en's Grothendieck-Riemann-Roch theorem, and explicitly compute the correction terms in the case of an orbifold surface with stabilizers of types ADE.
Keywords
Cite
@article{arxiv.2103.10767,
title = {Riemann-Roch coefficients for Kleinian orbisurfaces},
author = {Bronson Lim and Franco Rota},
journal= {arXiv preprint arXiv:2103.10767},
year = {2023}
}
Comments
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