  We determine the properties and leading instabilities of a spin liquid with a
Fermi surface passing near a van Hove singularity. Our study is motivated by
recent photoemission experiments on high $T_c$ cuprates in which it is found
that for the optimally doped material the experimental Fermi surface passes
near a van Hove singularity, while for underdoped materials, a pseudogap in the
electron spectral function is formed in the vicinity of the van Hove point. We
show theoretically that proximity to the van Hove singularity suppresses the
inelastic scattering due to the gauge field and permits the formation of a
d-wave RVB state in which the gap exists only near the van Hove points while
finite regions of the Fermi surface remain gapless. This $d$-wave pairing
provides a natural explanation of the pseudogap observed in photoemission. We
also discuss the relation of the pseudogap observed in the spectral function to
the pseudogaps observed in the magnetic susceptibility.
