The enumerative geometry of rth roots of line bundles is crucialin the theory of r-spin curves and occurs in the calculation ofGromov–Witten invariants of orbifolds. It requires the definition ofthe suitable compact moduli stack and the generalization of the standardtechniques from the theory of moduli of stable curves. In a previous paper, weconstructed a compact moduli stack by describing the notion of stability in thecontext of twisted curves. In this paper, by working with stable twisted curves,we extend Mumford’s formula for the Chern character of the Hodgebundle to the direct image of the universal rth root inK-theory.
