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Some L2 results for $\overline\partial$ on projective varieties with general singularities
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 131, Number 1, February 2009
- pp. 129-151
- 10.1353/ajm.0.0037
- Article
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Let $X$ be an irreducible $n$-dimensional projective variety in ${\Bbb C}P^N$ with arbitrary singular locus. We prove that the $L^2$-$\overline\partial$-$(p,1)$-cohomology groups (with respect to the Fubini-Study metric) of the regular part of $X$ are finite dimensional.