  We show that certain naturally arising cones over the main component of a
moduli space of $J_0$-holomorphic maps into $P^n$ have a well-defined euler
class. We also prove that this is the case if the standard complex structure
$J_0$ on $P^n$ is replaced by a nearby almost complex structure $J$. The
genus-zero analogue of the cone considered in this paper is always a vector
bundle. The genus-zero Gromov-Witten invariant of a projective hypersurface is
the euler class of such a vector bundle. As shown in a separate paper, this is
also the case for the "genus-one part" of the genus-one GW-invariant. The
remaining part is a multiple of the genus-zero GW-invariant.
