  We establish some facts about the behavior of the rational-geometric
subvariety of the $SL_2(\c)$ or $PSL_2(\c)$ character variety of a hyperbolic
knot manifold under the restriction map to the $SL_2(\c)$ or $PSL_2(\c)$
character variety of the boundary torus, and use the results to get some
properties about the A-polynomials and to prove the AJ conjecture for certain
class of knots in $S^3$ including in particular any $2$-bridge knot over which
the double branched cover of $S^3$ is a lens space of prime order.
