Partial compactifications of $ \mathcal{M}_{g,n}$

These are geometrically defined intermediate subvarieties between $ \mathcal{M}_{g,n}$ and $ \overline{\mathcal{M}}_{g,n}$ whose topology and tautological rings may also have a nice structure. They include the moduli space $ \mathcal{M}_{g,n}^{c}$ of curves of compact type (i.e. $ \overline{\mathcal{M}}_{g,n} - \Delta_0$, or those curves whose dual graph is a tree), $ \mathcal{M}_{g,n}^{\leq k}$ (curves with $ \leq k$ rational components), and $ \mathcal{M}_{g,n}^{\mathrm{rat}}$ (curves consisting of a single genus $ g$ component attached to trees of rational tails).

Jeffrey Herschel Giansiracusa 2005-06-27