2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130527We 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of the locally closed substacks of \bar{M}_{g,n}(X,β) corresponding to relative stable maps.This paper has been withdrawn.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 webpageAlgebraic Geometry14A20text