We investigate the interplay between lattice symmetry breaking and supercon
ducting order in a two-dimensional model of doped antiferromagnets, with lo
ng-range Coulomb interactions and Sp(2N) spin symmetry, in the large-N limi
t. Our results motivate the outline of a global phase diagram for the cupra
te superconductors. We describe the quantum transitions between the phases,
the evolution of their fermion excitation spectrum, and the experimental i
mplications.