Superconductivity in the cuprates

We evaluate numerically several superconducting correlation functions in a generalized $t-J$ model derived for hole-doped CuO$_2$ planes. The model includes a three-site term $t''$ similar to that obtained in the large $U$ limit of the Hubbard model but of opposite sign for realistic O-O hopping. For realistic parameters we obtain strong evidence of superconductivity of predominantly $d_{x^2-y^2}$ character. The ground state has a large overlap with a very simple resonating-valence-bond wave function with off-diagonal long-range order. This function reproduces the main features of the magnetic and superconducting correlation functions.