# Remarks on the $L^{2}$-cohomology of singular algebraic surfaces

@article{Nagase1989RemarksOT, title={Remarks on the \$L^\{2\}\$-cohomology of singular algebraic surfaces}, author={Masayoshi Nagase}, journal={Journal of The Mathematical Society of Japan}, year={1989}, volume={41}, pages={97-116} }

Let X be a normal singular algebraic surface (over C) embedded in the projective space PN(C) and let S be its singularity set, which consists of isolated singular points. By restricting the Fubini-Study metric of PN(C) to ' X-S, we obtain an incomplete Riemannian manifold (X, g). Then Hsiang-Pati asserted in [9] that the L2-cohomology H~2)() is naturally isomorphic to the dual of the middle intersection homology IH?(X), which is a special case of the conjecture due to Cheeger, Goresky and…

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