  The nef cone of a projective variety Y is an important and often elusive
invariant. In this paper we construct two polyhedral lower bounds and one
polyhedral upper bound for the nef cone of Y using an embedding of Y into a
toric variety. The lower bounds generalize the combinatorial description of the
nef cone of a Mori dream space, while the upper bound generalizes the
F-conjecture for the nef cone of the moduli space \bar{M}_{0,n} to a wide class
of varieties.
