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Give the smooth subset of a normal singular complex projective surface the metric induced from the ambient projective space. The L2 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 d -closed and 3-coclosed forms represent the classes of pure type in the corresponding Hodge decomposition of L2 cohomology.doi:10.1090/s0002-9947-1994-1191611-9 fatcat:24ay7shkyrdx7iajgl4bfepibq