  Given a degree one del Pezzo surface with canonical singularities, the linear
series generated by twice the anti-canonical divisor exhibits the surface as
the double cover of the quadric cone branched along a sextic curve. It is
natural to ask if this description extends to the boundary of a
compactification of the moduli space of degree one del Pezzo surfaces. The goal
of this paper is to show that this is indeed the case. In particular, we give
an explicit classification of the boundary of the moduli space of
anti-canonically polarized broken del Pezzo surfaces of degree one as double
covers of degenerations of the quadric cone.
