  Superconductivity in the cuprates exhibits many unusual features. We study
the two-dimensional Hubbard model with plaquette dynamical mean-field theory to
address these unusual features and relate them to other normal-state phenomena,
such as the pseudogap. Previous studies with this method found that upon doping
the Mott insulator at low temperature a pseudogap phase appears. The
low-temperature transition between that phase and the correlated metal at
higher doping is first-order. A series of crossovers emerge along the Widom
line extension of that first-order transition in the supercritical region. Here
we show that the highly asymmetric dome of the dynamical mean-field
superconducting transition temperature $T_c^d$, the maximum of the condensation
energy as a function of doping, the correlation between maximum $T_c^d$ and
normal-state scattering rate, the change from potential-energy driven to
kinetic-energy driven pairing mechanisms can all be understood as remnants of
the normal state first-order transition and its associated crossovers that also
act as an organizing principle for the superconducting state.
