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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Hodge decompositions and Dolbeault complexes on normal surfaces


Authors: Jeffrey Fox and Peter Haskell
Journal: Trans. Amer. Math. Soc. 343 (1994), 765-778
MSC: Primary 58G05; Secondary 14C30, 14F32, 32S60, 58A14
DOI: https://doi.org/10.1090/S0002-9947-1994-1191611-9
MathSciNet review: 1191611
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1994-1191611-9
Keywords: Normal surface, induced metric, $ {L^2}$ Dolbeault cohomology, Hodge decomposition
Article copyright: © Copyright 1994 American Mathematical Society