Riemann-Roch for algebraic stacks III; Virtual structure sheaves and virtual fundamental classes, by Roy Joshua

In this paper we apply the Riemann-Roch and Lefschtez-Riemann-Roch theorems proved in our earlier papers to define virtual fundamental classes for the moduli stacks of stable curves in great generality and establish various formulae for them.

Roy Joshua <joshua@math.ohio-state.edu>