An algebraic subvariety of the moduli space M_g is coarsely dense in the Teichmüller or Thurston metric if and only if it equals M_g, and this yields exact dimension criteria for dense projections of strata and orbit closures.
Degenerating families of R iemann surfaces
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Coarse density of subsets of $M_g$
An algebraic subvariety of the moduli space M_g is coarsely dense in the Teichmüller or Thurston metric if and only if it equals M_g, and this yields exact dimension criteria for dense projections of strata and orbit closures.