Using stacks to impose tangency conditions on curves
Abstract
Description
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This paper has been withdrawn.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
This paper has been withdrawn.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