These are
geometrically defined intermediate subvarieties between
and
whose topology and tautological rings may also have a nice
structure. They include the moduli space
of curves of
compact type (i.e.
, or those curves whose dual
graph is a tree),
(curves with rational
components), and
(curves consisting of a
single genus component attached to trees of rational tails).

Jeffrey Herschel Giansiracusa
2005-06-27