High-T c superconductivity and electronic band structure

We review the main results of the van Hove scenario applied to superconducting cuprates. It is based on the assumption that in these materials, the Fermi level lies near a singularity in the density of states (DOS). This hypothesis has recently been confirmed experimentally. We show that this model explains many properties of the high-T _c superconductors. We show that an anaogous model with a peak in the DOS may also be applied to the superconducting doped fullerenes. A general feature of the model is a very short coherence length.