𝐿²-Dolbeault complexes on singular curves and surfaces

Haskell, Peter

doi:10.1090/S0002-9939-1989-0975647-X

$L^ 2$-Dolbeault complexes on singular curves and surfaces
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Proc. Amer. Math. Soc. 107 (1989), 517-526 Request permission

Abstract:

Give the smooth part of a singular curve or normal surface the metric induced from the ambient projective space. On this incomplete manifold the minimal ${L^2}\bar \partial$-complex of $(0,q)$-forms has finite-dimensional cohomology groups. The Euler characteristic of this cohomology equals the Todd genus of any desingularization of the singular variety.

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