  We study two aspects of the physics of heterotic Line Bundle Standard Models
on smooth Calabi-Yau threefolds. First, we investigate to what degree modern
moduli stabilization scenarios can affect the standard model spectrum in such
compactifications. Specifically, we look at the case where some of the complex
structure moduli are fixed by a choice of hidden sector bundle. In this
context, we study the frequency with which the system tends to be forced to a
point in moduli space where the cohomology groups determining the spectrum in
the standard model sector jump in dimension. Second, we investigate to what
degree couplings, that are permitted by all of the obvious symmetries of the
theory, actually vanish due to certain topological constraints associated to
their higher dimensional origins. We find that both effects are prevalent
within the data set of heterotic Line Bundle Standard Models studied.
