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$ L\sp 2$-Dolbeault complexes on singular curves and surfaces


Author: Peter Haskell
Journal: Proc. Amer. Math. Soc. 107 (1989), 517-526
MSC: Primary 58G05
DOI: https://doi.org/10.1090/S0002-9939-1989-0975647-X
MathSciNet review: 975647
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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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DOI: https://doi.org/10.1090/S0002-9939-1989-0975647-X
Article copyright: © Copyright 1989 American Mathematical Society

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