  The two-dimensional repulsive Hubbard model has been investigated by a
variety of methods, from small to large U. Superconductivity with d-wave
symmetry is consistently found close to half filling. After a brief review of
the various methods a variational many-electron state is discussed in more
detail. This trial state is a natural extension of the Gutzwiller ansatz and
provides a substantial improvement thereof.

Strongly Correlated Electrons;Superconductivity