Hodge decompositions and Dolbeault complexes on normal surfaces

Abstract

Give the smooth subset of a normal singular complex projective surface the metric induced from the ambient projective space. The L 2 {L^2} cohomology of this incomplete manifold is isomorphic to the surface’s intersection cohomology, which has a natural Hodge decomposition. This paper identifies Dolbeault complexes whose ∂ ¯ \bar \partial -closed and ∂ ¯ \bar \partial -coclosed forms represent the classes of pure type in the corresponding Hodge decomposition of L 2 {L^2} cohomology.