  Large-scale structure projections are an obstacle in converting the shear
signal of clusters detected in weak-lensing maps into virial masses. However,
this step is not necessary for constraining cosmology with the shear-peak
abundance, if we are able to predict its amplitude. We generate a large
ensemble of N-body simulations spanning four cosmological models, with total
volume V~1 (Gpc/h)^3 per model. Variations to the matter density parameter and
amplitude of fluctuations are considered. We measure the abundance of peaks in
the mass density projected in ~100 Mpc/h slabs to determine the impact of
structures spatially correlated with the simulation clusters, identified by the
3D friends-of-friends algorithm. The halo model shows that the choice of the
smoothing filter for the density field is important in reducing the
contribution of correlated projections to individual halo masses. Such
contributions are less than 2% in the case of the optimal, compensated filter
used throughout this analysis. We measure the change in the mass of peaks when
projected in slabs of various thicknesses. Peaks in slabs of 26 Mpc/h and 102
Mpc/h suffer an average mass change of less than 2% compared to their mass in
slabs of 51 Mpc/h. We then explore the cosmology dependence of the
projected-peak mass function, and find that, for a wide range of slab
thicknesses (<500 Mpc/h), it scales with cosmology in exactly the same way as
the 3D friends-of-friends mass function and the Sheth-Tormen formula. This
extends the earlier result of Marian et al. (2009). Finally, we show that for
all cosmological models considered, the low and intermediate mass bins of the
peak abundance can be described using a modified Sheth-Tormen functional form
to within 10%-20% accuracy.
