Riemann–Roch coefficients for Kleinian orbisurfaces

Abstract

AbstractSuppose $$\mathcal {S}$$ S 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.