For families of log curves carrying a mesa structure, the selected subcurve can be contracted in a base-change-compatible way, yielding contractions between moduli spaces of curves.
existence of modifications, Annals of Mathematics 91 (1970), no
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Contractions of subcurves of families of log curves
For families of log curves carrying a mesa structure, the selected subcurve can be contracted in a base-change-compatible way, yielding contractions between moduli spaces of curves.