  Using lattice QCD we extract $\pi\pi$ scattering amplitudes with
isospin--0,1,2 in low partial-waves at two values of the light quark mass
corresponding to $m_\pi \sim 283$ and $330$ MeV. We confirm expectations of
weak repulsion in isospin--2, and the presence of a narrow $\rho$ resonance in
isospin--1, and study the pion mass dependence of these channels. In isospin--0
we find that the two pion masses considered straddle the point at which the
$\sigma$ transitions from being a stable bound-state to being either a virtual
bound-state or a subthreshold resonance. We discuss the ability of lattice
calculations like these to precisely determine the $\sigma$ pole location when
it is a resonance, and propose an approach in which the full complement of
amplitudes computed in this paper can be used simultaneously to provide more
constraint.
