Using stacks to impose tangency conditions on curves
arXiv:math/0312349
Abstract
We define a Deligne-Mumford stack X_{D,r} which depends on a scheme X, an effective Cartier divisor D\subset X, and a positive integer r. Then we show that the Abramovich-Vistoli moduli stack of stable maps into X_{D,r} provides compactifications of the locally closed substacks of \bar{M}_{g,n}(X,β) corresponding to relative stable maps.
This paper has been withdrawn. It was accepted by the American Journal of Mathematics in revised form and can be downloaded from the author's webpage