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Using stacks to impose tangency conditions on curves
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 129, Number 2, April 2007
- pp. 405-427
- 10.1353/ajm.2007.0007
- Article
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Abstract
We define a Deligne-Mumford stack XD,r which depends on a scheme X, an effective Cartier divisor D ⊂ X, and a positive integer r. Then we show that the Abramovich-Vistoli moduli stack of stable maps into XD,r provides compactifications of the locally closed substacks of M g,n(X, β) corresponding to relative stable maps.
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