Hodge decompositions and Dolbeault complexes on normal surfaces

Fox, Jeffrey; Haskell, Peter

doi:10.1090/S0002-9947-1994-1191611-9

Hodge decompositions and Dolbeault complexes on normal surfaces
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by Jeffrey Fox and Peter Haskell PDF

Trans. Amer. Math. Soc. 343 (1994), 765-778 Request permission

Abstract:

Give the smooth subset of a normal singular complex projective surface the metric induced from the ambient projective space. The ${L^2}$ 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 ${L^2}$ cohomology.

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