Stable twisted curves and their -spin structures
The subject of this article is the notion of -spin structure: a line bundle whose th power is isomorphic to the canonical bundle. Over the moduli functor of smooth genus- curves, -spin structures form a finite torsor under the group of -torsion line bundles. Over the moduli functor of stable curves, -spin structures form an étale stack, but both the finiteness and the torsor structure are lost.In the present work, we show how this bad picture can be definitely improved just by placing...