  We establish sufficient conditions for extension of weighted square
integrable holomorphic functions from a possibly singular hypersurface to the
ambient affine space. The norms we use are the so-called Bargmann-Fock norms,
and thus there are restrictions on the singularities and the density of the
hypersurface. Our sufficient conditions are that it has density less than 1,
and is uniformly flat in a sense that extends to singular varieties the notion
of uniform flatness introduced earlier. We present an example of Ohsawa showing
that uniform flatness is not necessary for extension in the singular case, and
find an example showing that, for rather different reasons, it is also not
necessary for the smooth case. The latter answers in the negative a question
posed in an earlier paper of the second author.
