The boundary of
is the
complement of the open subset
. It is of pure (complex)
codimension 1. It consists of irreducible components
,
where a generic curve in
is a
(geometric) genus curve with a single node and a generic curve
in
consists of a genus curve attached to a
genus curve at a single node. Each boundary divisor is a
finite-group quotient of a product of
's for and
. The subspace
is called the locus of
curves of compact type.

Jeffrey Herschel Giansiracusa
2005-06-27