Projected Wavefunctions and High Temperature Superconductivity

We study the Hubbard model with parameters relevant to the cuprates, using variational Monte Carlo with projected d-wave states. For doping 0 < x < 0.35 we obtain a superconductor whose order parameter tracks the observed nonmonotonic Tc(x). The variational parameter Delta_{var}(x) scales with the (pi,0) ``hump'' and T* seen in photoemission. Projection leads to incoherence in the spectral function, and from the singular behavior of its moments we obtain the nodal quasiparticle weight Z which vanishes linearly in x, though the Fermi velocity remains finite as x approaches zero. The Drude weight D_{low} and superfluid density are consistent with experiments, and D_{low} scales with Z.