Some L2 results for d-bar on projective varieties with general   singularities
  Let X be an irreducible n-dimensional projective variety in CP^N with arbitrary singular locus. We prove that the L2-(p,1)-d-bar cohomology groups (with respect to the Fubini-Study metric) of the regular part of X are finite dimensional. 
Nils Ovrelid and Sophia Vassiliadou