Using stacks to impose tangency conditions on curves

Details Using stacks to impose tangency conditions on curves Using stacks to impose tangency conditions on curves

2003-12-18

arxiv.org/abs/math/0312349v4

Amer. J. Math. 129 (2007) 405-427

Mathematics

Algebraic Geometry

This paper has been withdrawn. It was accepted by the American Journal of Mathematics in revised form and can be downloaded fr

Scientific paper

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,\beta)
corresponding to relative stable maps.

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