  In this paper we resolve the degree-2 Abel map for nodal curves. Our results
are based on a previous work of the authors reducing the problem of the
resolution of the Abel map to a combinatorial problem via tropical geometry. As
an application, we characterize when the (symmetrized) degree-2 Abel map is not
injective, a property that, for a smooth curve, is equivalent to the curve
being hyperelliptic.
